The main purpose of this paper is to prove the following result: Let R be a 2-torsion free semiprime *-ring. Suppose that θ, φ are endomorphisms of R such that θ is onto. If there exists an additive mapping F: R → R associated with a (θ,... more
The main purpose of this paper is to prove the following result: Let R be a 2-torsion free semiprime *-ring. Suppose that θ, φ are endomorphisms of R such that θ is onto. If there exists an additive mapping F: R → R associated with a (θ, φ)-derivation d of R such that F(xx*) = F(x)θ(x*) + φ(x)d(x*) holds for all x ∈ R, then F is a generalized (θ, φ)-derivation. Further, some more related results are obtained.
In this paper, it is defined that left *-α-derivation, generalized left *-α-derivation and *-α-derivation, generalized *-α-derivation of a *-ring where α is a homomorphism. The results which proved for generalized left *-derivation of R... more
In this paper, it is defined that left *-α-derivation, generalized left *-α-derivation and *-α-derivation, generalized *-α-derivation of a *-ring where α is a homomorphism. The results which proved for generalized left *-derivation of R in [1] are extended by using generalized left *-α-derivation. The commutativity of a *-ring with generalized left *-α-derivation is investigated and some results are given for generalized *-α-derivation.
In the theory of rings and modules there is a correspondence between certain ideals of a ring R and submodules of an R-module that arise from annihilation. The submodules obtained using annihilation, which correspond to prime ideals play... more
In the theory of rings and modules there is a correspondence between certain ideals of a ring R and submodules of an R-module that arise from annihilation. The submodules obtained using annihilation, which correspond to prime ideals play an important role in decomposition theory. In this paper, we attempt to intuitionistic fuzzify the concept of annihilators of subsets of modules. We investigate certain characterization of intuitionistic fuzzy annihilators of subsets of modules. Using the concept of intuitionistic fuzzy annihilators, intuitionistic fuzzy prime submodules and intuitionistic fuzzy annihilator ideals are defined and various related properties are established. KEYWORDS Intuitionistic fuzzy submodule, intuitionistic fuzzy prime submodule, intuitionistic fuzzy ideal, intuitionistic fuzzy annihilator, semiprime ring.
In this study, we prove that any nonzero reverse (,) − biderivation on a prime ring is (,) − biderivation. Also, we show that any Jordan (,) − biderivation on non-commutative semi-prime ring with ℎ () ≠ 2 is an (,) − biderivation. In... more
In this study, we prove that any nonzero reverse (,) − biderivation on a prime ring is (,) − biderivation. Also, we show that any Jordan (,) − biderivation on non-commutative semi-prime ring with ℎ () ≠ 2 is an (,) − biderivation. In addition, we investigate commutative feature of prime ring with Jordan left (,) − biderivation.
