In this paper, a special class of rings for which an element a in R, satisfying the additional pr... more In this paper, a special class of rings for which an element a in R, satisfying the additional property an=an−1+an−1, for an integer n>1 is introduced and several results and examples related to this special class of rings is presented.
The aim of this paper is to study the theory of fuzzy quasi-ideals in near-algebra, and obtain so... more The aim of this paper is to study the theory of fuzzy quasi-ideals in near-algebra, and obtain some characterizations.
International Journal of Scientific and Innovative Mathematical Research, 2017
The important concept of fuzzy set has been introduced by L.A. Zadeh [14] in 1965. Since then man... more The important concept of fuzzy set has been introduced by L.A. Zadeh [14] in 1965. Since then many papers on fuzzy sets appeared showing its importance in the field of mathematics. The notion of a fuzzy subset was introduced by Zadeh [14] and then fuzzy subsets have been applied to various branches of mathematics. Near-rings are one of the generalized structures of rings. W.J. Liu [3] has studied fuzzy invariant subgroups and fuzzy ideals. In1998 S. D. Kim and H. S. kim [2] has been introduced analogue of fuzzy ideals of near-rings. G. Pilz [9] introduced near-rings and in 1971 Rosenfeld [11] initiated the study of fuzzy subgroups. In [4] M. Muralikrishna Rao studied T-fuzzy ideal in ordered T-semi rings. In [10] A. Radha Krishna and M. Bandari defined the partially ordered (P.O) near-ring. M. Akram[l] introduced the notion of fuzzy ideals in near-rings with respect to a tnorm T. In [12] Bh. Satyanarayana introduced -near-rings. T. Srinivas and T. Nagaiah [13] introduced the notion of T-fuzzy ideals of -near-rings and investigated some of their properties. After that T. Nagaiah et al. [5, 6, 7] studied fuzzy ideals of partially ordered -semi groups and anti fuzzy ideals in near-ring. In [8] T. Nagaiah and L. Bhaskar introduced the notion of T-fuzzy ideal of PON. In this direction we study the fuzzy ideals of partially ordered near-rings. 2. PRELIMINARIES For the sake of continuity we recall the following definitions. Definition 1.A non-empty set N with two binary operations "+" and "•" is called a near-ring if (i) (N, +) is a group (not necessarily abelian) (ii) (N, •) is a semi group (iii) x• (y + z) = x • y + x • z for all x, y, z N. We will use the word "near-ring" to mean "left near-ring".
In the present paper we introduce the concept on sum of fuzzy ideals of a Γ-near-ring and the sum... more In the present paper we introduce the concept on sum of fuzzy ideals of a Γ-near-ring and the sum of anti fuzzy ideals of a Γ-near-ring. 2010 AMS Classification: 16Y30, 03E72
Zenodo (CERN European Organization for Nuclear Research), Jun 29, 2022
The notion of neutrosophic algebra, ideal of neutrosophic algebra, kernel and neutrosophic quotie... more The notion of neutrosophic algebra, ideal of neutrosophic algebra, kernel and neutrosophic quotient algebra have been proposed in this paper. We characterize some properties of neutrosophic algebra and proved that every quotient neutrosophic algebra is quotient algebra. Also we proved that every neutrosophic algebra is algebra and direct product of neutrosophic algebras over a neutrosophic field is algebra.
Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the ... more Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the concept of bipolar fuzzy quasi ideals and bipolar N subgroups of near rings are introduced. Pertaining to this notion we also introduced some basic definitions, theoretical properties and characterizations of bipolar fuzzy quasi ideals.
In this paper the notion of residue class of -near-rings and interval valued anti fuzzy ideals of... more In this paper the notion of residue class of -near-rings and interval valued anti fuzzy ideals of -near-rings is introduced. Homomorphism and endomorphism of interval-valued anti fuzzy ideal in -near-rings is discussed. Also union of interval valued -near rings, image and pre-image of interval valued -near-rings with respect to anti fuzzy ideals are studied. AMS subject classification: 16Y30, 03E72.
The notions of partially ordered Γ-near-ring(POGN), T-fuzzy ideal of POGN(TFIPOGN), T-fuzzy K-ide... more The notions of partially ordered Γ-near-ring(POGN), T-fuzzy ideal of POGN(TFIPOGN), T-fuzzy K-ideal of a POGN(TFKIPOGN), quotient POGN, and normal TFKIPOGN are introduced and investigated the basic properties. I also propose some necessary sufficient conditions on POGN under the T-norm.
In this paper we establish the few relations on cen tral loops and we investigate the central loo... more In this paper we establish the few relations on cen tral loops and we investigate the central loops are power associative. The commut ative left central loops if and only if they are right central loops. We also establish the central loops representation is alternative and flexible. Andrew Rajah and Chong K am Yoon are proved the construction of M (G, 2), the Moufang loops are isomorphic to M (G, 2). It is an important note that we are extended the previous work Andrew Rajah (11) , the Central loops are isomorphic to C (G, 2) .
The notions of fuzzy ideal of a partially ordered nearring(PON), T-fuzzy ideal of PON, T-fuzzy K-... more The notions of fuzzy ideal of a partially ordered nearring(PON), T-fuzzy ideal of PON, T-fuzzy K-ideal of PON and fuzzy magnified translation have been proposed in this paper. Characterization of partially ordered near-ring in terms of fuzzy ideals has been obtained.
In this paper, we characterize the relationship between fuzzy ideals, fuzzy interior ideals, fuzz... more In this paper, we characterize the relationship between fuzzy ideals, fuzzy interior ideals, fuzzy bi-ideals and the characteristic function of fuzzy ideals in PO-G-semigroups. Also we proved the equivalent statements, necessary and suf cient conditions on partial ordered Gsemigroups.
In this paper the notion of fuzzy ideals of a Γ-near-ring with respect to a t-norm is introduced ... more In this paper the notion of fuzzy ideals of a Γ-near-ring with respect to a t-norm is introduced and investigated some related properties. This concept of T-fuzzy ideals of a Γ-near-ring is a generalization of the concept of T-fuzzy ideals in near-rings. Also the notions of T-fuzzy ideals of a Γ-near-ring, quotient Γ-near-ring with respect to a t-norm and the sum of T-fuzzy ideals of a Γ-near-ring are introduced. Further, it is shown that an onto homomorphic image of a T-fuzzy ideal with Sup property is a Tfuzzy ideal and an epimorphic pre-image of a T-fuzzy ideal of a Γ-near-ring is a T-fuzzy ideal.
... { } { } { My iyf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf,, , /) inf { } )(, yf xf Max i i Λ Λ =... more ... { } { } { My iyf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf,, , /) inf { } )(, yf xf Max i i Λ Λ = (ii) Let x, y, z∈M and Γ ∈ β α, then we have ( ) ) (zyxf zyxA i i β α β α Λ = I = { } Mzx izfxf i i ∈ Λ ∈ , /)( inf { } { } { Mz izf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf, , /)( inf { } )( , zf xf Max i i Λ Λ = ...
Abstract. The characterizations of h-semisimple hemirings are first discussed based on soft set t... more Abstract. The characterizations of h-semisimple hemirings are first discussed based on soft set theory. Then notions of soft h-hemiregular hemirings, soft h-intra-hemiregular hemirings and soft h-semisimple hemirings are introduced and some properties of them are ...
RECENT TRENDS IN PURE AND APPLIED MATHEMATICS, 2019
In this research article, we introduce the notion of sum and direct sum of vague ideals of a near... more In this research article, we introduce the notion of sum and direct sum of vague ideals of a near-ring and developed some results related to the vague ideals of a near-ring with suitable example.In this research article, we introduce the notion of sum and direct sum of vague ideals of a near-ring and developed some results related to the vague ideals of a near-ring with suitable example.
Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the ... more Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the concept of bipolar fuzzy quasi ideals and bipolar N subgroups of near rings are introduced. Pertaining to this notion we also introduced some basic definitions, theoretical properties and characterizations of bipolar fuzzy quasi ideals.
In this paper, we introduce the concept of sum and direct sum of vague ideals of gamma near-ring ... more In this paper, we introduce the concept of sum and direct sum of vague ideals of gamma near-ring and also discuss some related properties of vague ideals of gamma near-ring.
In this paper, a special class of rings for which an element a in R, satisfying the additional pr... more In this paper, a special class of rings for which an element a in R, satisfying the additional property an=an−1+an−1, for an integer n>1 is introduced and several results and examples related to this special class of rings is presented.
The aim of this paper is to study the theory of fuzzy quasi-ideals in near-algebra, and obtain so... more The aim of this paper is to study the theory of fuzzy quasi-ideals in near-algebra, and obtain some characterizations.
International Journal of Scientific and Innovative Mathematical Research, 2017
The important concept of fuzzy set has been introduced by L.A. Zadeh [14] in 1965. Since then man... more The important concept of fuzzy set has been introduced by L.A. Zadeh [14] in 1965. Since then many papers on fuzzy sets appeared showing its importance in the field of mathematics. The notion of a fuzzy subset was introduced by Zadeh [14] and then fuzzy subsets have been applied to various branches of mathematics. Near-rings are one of the generalized structures of rings. W.J. Liu [3] has studied fuzzy invariant subgroups and fuzzy ideals. In1998 S. D. Kim and H. S. kim [2] has been introduced analogue of fuzzy ideals of near-rings. G. Pilz [9] introduced near-rings and in 1971 Rosenfeld [11] initiated the study of fuzzy subgroups. In [4] M. Muralikrishna Rao studied T-fuzzy ideal in ordered T-semi rings. In [10] A. Radha Krishna and M. Bandari defined the partially ordered (P.O) near-ring. M. Akram[l] introduced the notion of fuzzy ideals in near-rings with respect to a tnorm T. In [12] Bh. Satyanarayana introduced -near-rings. T. Srinivas and T. Nagaiah [13] introduced the notion of T-fuzzy ideals of -near-rings and investigated some of their properties. After that T. Nagaiah et al. [5, 6, 7] studied fuzzy ideals of partially ordered -semi groups and anti fuzzy ideals in near-ring. In [8] T. Nagaiah and L. Bhaskar introduced the notion of T-fuzzy ideal of PON. In this direction we study the fuzzy ideals of partially ordered near-rings. 2. PRELIMINARIES For the sake of continuity we recall the following definitions. Definition 1.A non-empty set N with two binary operations "+" and "•" is called a near-ring if (i) (N, +) is a group (not necessarily abelian) (ii) (N, •) is a semi group (iii) x• (y + z) = x • y + x • z for all x, y, z N. We will use the word "near-ring" to mean "left near-ring".
In the present paper we introduce the concept on sum of fuzzy ideals of a Γ-near-ring and the sum... more In the present paper we introduce the concept on sum of fuzzy ideals of a Γ-near-ring and the sum of anti fuzzy ideals of a Γ-near-ring. 2010 AMS Classification: 16Y30, 03E72
Zenodo (CERN European Organization for Nuclear Research), Jun 29, 2022
The notion of neutrosophic algebra, ideal of neutrosophic algebra, kernel and neutrosophic quotie... more The notion of neutrosophic algebra, ideal of neutrosophic algebra, kernel and neutrosophic quotient algebra have been proposed in this paper. We characterize some properties of neutrosophic algebra and proved that every quotient neutrosophic algebra is quotient algebra. Also we proved that every neutrosophic algebra is algebra and direct product of neutrosophic algebras over a neutrosophic field is algebra.
Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the ... more Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the concept of bipolar fuzzy quasi ideals and bipolar N subgroups of near rings are introduced. Pertaining to this notion we also introduced some basic definitions, theoretical properties and characterizations of bipolar fuzzy quasi ideals.
In this paper the notion of residue class of -near-rings and interval valued anti fuzzy ideals of... more In this paper the notion of residue class of -near-rings and interval valued anti fuzzy ideals of -near-rings is introduced. Homomorphism and endomorphism of interval-valued anti fuzzy ideal in -near-rings is discussed. Also union of interval valued -near rings, image and pre-image of interval valued -near-rings with respect to anti fuzzy ideals are studied. AMS subject classification: 16Y30, 03E72.
The notions of partially ordered Γ-near-ring(POGN), T-fuzzy ideal of POGN(TFIPOGN), T-fuzzy K-ide... more The notions of partially ordered Γ-near-ring(POGN), T-fuzzy ideal of POGN(TFIPOGN), T-fuzzy K-ideal of a POGN(TFKIPOGN), quotient POGN, and normal TFKIPOGN are introduced and investigated the basic properties. I also propose some necessary sufficient conditions on POGN under the T-norm.
In this paper we establish the few relations on cen tral loops and we investigate the central loo... more In this paper we establish the few relations on cen tral loops and we investigate the central loops are power associative. The commut ative left central loops if and only if they are right central loops. We also establish the central loops representation is alternative and flexible. Andrew Rajah and Chong K am Yoon are proved the construction of M (G, 2), the Moufang loops are isomorphic to M (G, 2). It is an important note that we are extended the previous work Andrew Rajah (11) , the Central loops are isomorphic to C (G, 2) .
The notions of fuzzy ideal of a partially ordered nearring(PON), T-fuzzy ideal of PON, T-fuzzy K-... more The notions of fuzzy ideal of a partially ordered nearring(PON), T-fuzzy ideal of PON, T-fuzzy K-ideal of PON and fuzzy magnified translation have been proposed in this paper. Characterization of partially ordered near-ring in terms of fuzzy ideals has been obtained.
In this paper, we characterize the relationship between fuzzy ideals, fuzzy interior ideals, fuzz... more In this paper, we characterize the relationship between fuzzy ideals, fuzzy interior ideals, fuzzy bi-ideals and the characteristic function of fuzzy ideals in PO-G-semigroups. Also we proved the equivalent statements, necessary and suf cient conditions on partial ordered Gsemigroups.
In this paper the notion of fuzzy ideals of a Γ-near-ring with respect to a t-norm is introduced ... more In this paper the notion of fuzzy ideals of a Γ-near-ring with respect to a t-norm is introduced and investigated some related properties. This concept of T-fuzzy ideals of a Γ-near-ring is a generalization of the concept of T-fuzzy ideals in near-rings. Also the notions of T-fuzzy ideals of a Γ-near-ring, quotient Γ-near-ring with respect to a t-norm and the sum of T-fuzzy ideals of a Γ-near-ring are introduced. Further, it is shown that an onto homomorphic image of a T-fuzzy ideal with Sup property is a Tfuzzy ideal and an epimorphic pre-image of a T-fuzzy ideal of a Γ-near-ring is a T-fuzzy ideal.
... { } { } { My iyf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf,, , /) inf { } )(, yf xf Max i i Λ Λ =... more ... { } { } { My iyf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf,, , /) inf { } )(, yf xf Max i i Λ Λ = (ii) Let x, y, z∈M and Γ ∈ β α, then we have ( ) ) (zyxf zyxA i i β α β α Λ = I = { } Mzx izfxf i i ∈ Λ ∈ , /)( inf { } { } { Mz izf Mx ixf Max i i ∈ Λ ∈ ∈ Λ ∈ ≤ , /) inf, , /)( inf { } )( , zf xf Max i i Λ Λ = ...
Abstract. The characterizations of h-semisimple hemirings are first discussed based on soft set t... more Abstract. The characterizations of h-semisimple hemirings are first discussed based on soft set theory. Then notions of soft h-hemiregular hemirings, soft h-intra-hemiregular hemirings and soft h-semisimple hemirings are introduced and some properties of them are ...
RECENT TRENDS IN PURE AND APPLIED MATHEMATICS, 2019
In this research article, we introduce the notion of sum and direct sum of vague ideals of a near... more In this research article, we introduce the notion of sum and direct sum of vague ideals of a near-ring and developed some results related to the vague ideals of a near-ring with suitable example.In this research article, we introduce the notion of sum and direct sum of vague ideals of a near-ring and developed some results related to the vague ideals of a near-ring with suitable example.
Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the ... more Bipolar fuzzy set is the generalization of fuzzy set. Based on the bipolar fuzzy set theory, the concept of bipolar fuzzy quasi ideals and bipolar N subgroups of near rings are introduced. Pertaining to this notion we also introduced some basic definitions, theoretical properties and characterizations of bipolar fuzzy quasi ideals.
In this paper, we introduce the concept of sum and direct sum of vague ideals of gamma near-ring ... more In this paper, we introduce the concept of sum and direct sum of vague ideals of gamma near-ring and also discuss some related properties of vague ideals of gamma near-ring.
Advances in Algebra and Analysis, Trends in Mathematics - Proceedings Book (1), 2018
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
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