Homomorphism

Basically, the connection of two many-sorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider variants of the basic connection scheme. Our results can be seen as a generalization of the so-called -connection approach for combining modal logics to an algebraic setting.

In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related.

This article presents some of the main points of the study for the practical application of various hyperoperations in engineering practice. The authors examined the use of hyperoperations in mathematical formalization of analytical solutions of branching algorithms, the use of new number formats for encoding information based on large numbers. The methods of applying hyperoperations considered by the authors allow them to be effectively used on modern microprocessor-based computers with a built-in mathematical coprocessor, which is an integral part of the processor core, which allows implementing algorithms based on operations of the order higher than “addition” and “subtraction

Abstract. We define the stability of a subgroup under a class of maps, and establish the basic prop-erties of this notion. Loosely speaking, we will say that a normal subgroup, or more generally a normal series {An} of a group A, is stable under a class of homomorphisms H if ...

In this article, a new notion of $n$-Jordan homomorphism namely the mixed $n$-Jordan homomorphism is introduced. It is proved that how a mixed $(n+1)$-Jordan homomorphism can be a mixed $n$-Jordan homomorphism and vice versa. By means of some examples, it is shown that the mixed $n$-Jordan homomorphisma are different from the $n$-Jordan homomorphisms and the pseudo $n$-Jordan homomorphisms. As a consequence, it shown that every mixed Jordan homomorphism from Banach algebra $\mathcal{A}$ into commutative semisimple Banach algebra $\mathcal{B}$ is automatically continuous. Under some mild conditions, every unital pseudo $3$-Jordan homomorphism can be a homomorphism.

This paper proposes a definition of a fuzzy partition element based on the homomorphism between type-1 fuzzy sets and the three-valued Kleene algebra. A new clustering method based on the C-means algorithm, using the defined partition, is presented in this paper, which will be validated with the traditional iris clustering problem by measuring its petals.

Let G be a topological group which acts in a continuous and transitive way on a topological space M. Sufficient conditions are given that assure that, for every m∈ M, the map from G onto M defined by g↦→ g· m is an open map. Some consequences of the ...