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Rings with the double centralizer property [PDF]

Journal of Algebra, 1972
Dlab V, Ringel CM. Rings with the double centralizer property. Journal of algebra.
Vlastimil Dlab
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Centralizer Near-Rings Determined by Unions of Groups

Results in Mathematics, 1987
Let \(P=\{G_{\alpha}\); \(\alpha\in A\}\) be a set of disjoint groups, \(X=\cup_{\alpha \in A}G_{\alpha}\). Let S be a monoid of functions on X such that \(\sigma\in S\) induces homomorphisms from each \(G_{\alpha}\) to some \(G_{\beta}\). Define \(M_ S(X,P)=\{f: X\to X\); \(f(G_{\alpha})\subseteq G_{\alpha}\) for all \(\alpha\in A\), \(f\sigma =\sigma
Fuchs, Peter, Maxson, C. J., Smith, K. C.   +2 more
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When is a centralizer near-ring isomorphic to a matrix near-ring? Part 2

2001
Let G be a finite group and A a group of automorphisms of G. It is always the case that for every integer n ≥ 2 the matrix near-ring \( \mathbb{M}_n \)(M A (G);G) is a subnear-ring of the centralizer near-ring M A (G n ). We find conditions such that \( \mathbb{M}_n \)(M A (G);G) is a proper subset of M A (G n ).
Alan Oswald, Kirby C. Smith, Leon van Wyk   +2 more
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Lie (Jordan) Centralizer on Graded Rings

Symmetry
In this paper, we provide the necessary and sufficient conditions for a Lie centralizer to be proper and a Jordan centralizer to be a centralizer on graded rings.
Qikai Wang, Haiyan Zhu, Haoting He
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NEAR-RINGS WITH P-CENTRAL P-NILPOTENT OR P IDEMPOTENT ELEMENTS

JP Journal of Algebra, Number Theory and Applications, 2018
Summary: Let \(P\) be an ideal of a near-ring. In this study, we introduce \(P\)-nilpotent element of a near-ring with properties. Also, we show that each element which of both \(P\)-nilpotent and \(P\)-idempotent is only an element of the ideal \(P\).
Kamacı, Hüseyin, Atagün, Akın Osman
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Centraliser near-rings determined by fixed point free automorphism groups

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1987
SynopsisLet G be a group and let A be a fixed point free group of automorphisms of G. It is shown that the centraliser near-ring MA(G) has at most one nontrivial ideal. Conditions on the pair (A, G) are given which force MA(G) to be simple. It is shown that if a nonsimple near-ring MA(G) exists, then A and G have unusual properties.
Fuchs, Peter, Maxson, C. J., Pettet, M. R., Smith, K. C.   +3 more
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The centralizer near-ring of an inverse semigroup of endomorphisms of a group

Communications in Algebra, 1995
Let G be a group and S an inverse semigroup of endomorphisms of G. The simplicity of the centralizer near- ring MS(G) = {fe M(G)‖foα = αo f, ∀αeS} is characterized. The necessary and sufficient conditions are given for simplicity of Ms(G) in terms of the structure of G and S.
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Centralizer Near-Rings Determined by End g

1995
Let G be a group. The structure of the centralizer near-ring M E (G) = {f: G → G | fσ = σf for every σ ∈ End G} is investigated for the cases in which G is a finitely generated abelian, characteristically simple, symmetric or generalized quaternion group.
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Commutativity and Centrality Conditions Induced By Generalized Skew Derivations on Prime and Semiprime Near-Rings

International Journal of Research and Scientific Innovation
In this paper, we investigate the influence of generalized skew derivations on the structural properties of prime and semiprime near-rings. In particular, we establish several new commutativity and centrality conditions arising from differential identities involving generalized skew derivations associated with automorphisms.
Tasiu Abdullahi Yusuf, Abdu Madugu
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A STUDY ON NEAR-RINGS WITH SEMI-CENTRAL IDEMPOTENTS

Far East Journal of Mathematical Sciences (FJMS), 2015
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