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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Characterizing series for faithful d.g. near-rings


Authors: J. D. P. Meldrum and C. Lyons
Journal: Proc. Amer. Math. Soc. 72 (1978), 221-227
MSC: Primary 16A76
DOI: https://doi.org/10.1090/S0002-9939-1978-0507312-X
MathSciNet review: 507312
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Abstract: Let (R, S) be a distributively generated near ring satisfying $ (R,S) \subseteq (E(G),{\text{End}}(G))$ and $ S \subseteq {\text{End}}(G)$ for some group G, endomorphism near ring $ E(G)$, and subsemigroup S of the endomorphisms of G, $ {\text{End}}(G)$. The radicals $ J(R)$ of (R, S) are characterized in terms of series of subgroups of G. We assume S contains the inner automorphisms of G and obtain two main results on characterizing series. (1) If G satisfies both chain conditions on S subgroups then a unique minimal characterizing series exists. (2) If G is finite, then both maximal and minimal characterizing series exist, are unique, and are themselves characterized in G.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0507312-X
Keywords: Faithful representation of distributively near rings, endomorphism near rings, radicals, composition series
Article copyright: © Copyright 1978 American Mathematical Society