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The analysis of homomorphism between near rings is the main notion of our research. We characterize homomorphism in intuitionistic fuzzy weak bi ideals of near rings which is the generalized concept of homomorphism in fuzzy weak bi ideals. In addition, we study some of their basic properties.

Integrates the concept of an m-semilattice with the theory of soft sets, and introduces definitions for soft m-semilattices, soft sub-m-semilattices, soft ideals, and ideal soft m-semilattices. Several algebraic properties of soft m-semilattice are proved, especially those after combining the concepts of intersection, union, and direct product of soft sets. After establishing the definition of soft m-semilattice homomorphism, the relationship between m-semilattice homomorphism, m-semilattice isomorphism, soft m-semilattice homomorphism and soft m-semilattice, soft sub m-semilattice, soft ideal, ideal soft m-semilattice is studied.

‎In this paper‎, ‎we introduce the concepts of homomorphism of type 1‎, ‎2 and 3 and good homomorphism‎. ‎Then we investigate some properties of them‎.

The authors introduce the concept of finitely coloured equivalence for unital ^*-homomorphisms between \\mathrm C^*-algebras, for which unitary equivalence is the 1-coloured case. They use this notion to classify ^*-homomorphisms from separable, unital, nuclear \\mathrm C^*-algebras into ultrapowers of simple, unital, nuclear, \\mathcal Z-stable \\mathrm C^*-algebras with compact extremal trace space up to 2-coloured equivalence by their behaviour on traces; this is based on a 1-coloured classification theorem for certain order zero maps, also in terms of tracial data. As an application the authors calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, \\mathcal Z-stable \\mathrm C^*-algebras with compact extremal trace space: it is 1. In the case that the extremal trace space also has finite topological covering dimension, this confirms the remaining open implication of the Toms-Winter conjecture. Inspired by homotopy-rigidity theorems in geometry and topology, the authors derive a \"homotopy equivalence implies isomorphism\" result for large classes of \\mathrm C^*-algebras with finite nuclear dimension.

We study homomorphisms from Kaehler groups to Coxeter groups. As an application, we prove that a cocompact complex hyperbolic lattice (in complex dimension at least 2) does not embed into a Coxeter group or a right-angled Artin group. This is in contrast with the case of real hyperbolic lattices.

For cyclically ordered groups G, G’, the mapping f: G → G’ is called a homomorphism, if f is a homomorphism with respect to the group operation, and whenever x,y,z in G such that [x,y,z], and f(x), f(y), f(z), are distinct, then [f(x), f(y), f(z)]. In this paper, it will be given some conditions related to group homomorphisms.

In this paper we study Hurwitz spaces parameterizing coverings with special points and with monodromy group a Weyl group of type 𝐵𝑑. We prove that such spaces are irreducible if 𝑘 > 3𝑑 − 3. Here, 𝑘 denotes the number of local monodromies that are reflections relative to long roots.

Let ℳ be a Hilbert C∗-module. A linear mapping ψ : ℳ→ ℳ is said to be a Hilbert C∗-module Jordan homomorphism on ℳ if it satisfies the equation ψ(〈a, b〉a)= 〈ψ(a),ψ(b)〉 ψ(a) for all a, b ∈ℳ. In thispaper,we show that if ℳ is prime, then every Hilbert C∗-module Jordan homomorphism ψ from ℳ onto ℳ is a Hilbert C∗-module homomorphism or a Hilbert C∗-module anti-homomorphism on ℳ. We also prove a similar result about generalized Hilbert C∗-module Jordan homomorphism.

From the concepts of clean index of rings, nil clean index of rings, and weakly nil clean index of rings, we expand them by introducing the new concept, that is, trinil clean index of a ring. From any element a of a ring R with unity, we set τ( a ): = e ∈ R | e 3 = e and a − e ∈ Nil ( R ), where Nil( R ) is the set of all nilpotent elements of R ; trinil clean index of R is defined by sup|τ( a )|| a ∈ R and it is denoted by Trinin(R) . In this article, it will be investigated some properties of trinil clean index of any ring, ring homomorphism, and direct product. Some applications of determining trinil clean index of integral domains are also provided. We also determined the trinil clean index of ℤ n .

In this paper, we introduce the notion of hesitant fuzzy( correlation) MP filters, some properties and equivalent conditions are investigated. The relationships between hesitant fuzzy MP filter and hesitant fuzzy correlation MP filter is disscussed. Finally, we prove the invariance between the image and the original image of hesitant fuzzy correlation filter is studied under the premise of homomorphism.