Results 21 to 30 of about 54 (38)

Rings which are a Homomorphic Image of a Centralizer Near-Ring

1995
In this work the near-rings under consideration will be exclusively centralizer near-rings M A(G) where G is a finite group and A is a group of automorphisms of G.
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The group of units of centralizer near-rings

Communications in Algebra, 1984
J.R. Clay, C.J. Maxson, J.D.P. Meldrum
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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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Centralizer near-rings determined by PID-modules, II

Periodica Mathematica Hungarica, 1993
[For part I cf. Arch. Math. 56, No. 2, 140-147 (1991; Zbl 0706.16026).] The authors answer an open problem in radical theory by giving an example of a zero-symmetric simple near-ring with identity such that \(J_ 2(N) = N\). This is in contrast to the situation for rings, since every simple ring with identity is semisimple in the sense of Jacobson.
Fuchs, P., Maxson, C. J., van der Walt, A. P. J., Kaarli, K.   +3 more
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Centralizer near-rings determined by PID-modules

Archiv der Mathematik, 1991
Let G be a finitely generated module over a principal ideal domain D and let \(M_ D(G)\) be the centralizer near-ring determined by \(G_ D\). Structural properties of \(M_ D(G)\) such as simplicity and semisimplicity are characterized in terms of the invariants of \(G_ D\).
Fuchs, Peter, Maxson, C. J.
openaire   +2 more sources

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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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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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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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.
openaire   +1 more source