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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Strongly $ \pi$-regular matrix semigroups


Author: Jan Okniński
Journal: Proc. Amer. Math. Soc. 93 (1985), 215-217
MSC: Primary 20M10
MathSciNet review: 770522
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Abstract: We prove that if $ S$ is a strongly $ \pi $-regular multiplicative sub-semigroup of the matrix algebra $ {M_n}(K)$, $ K$ being a field, then there exists a chain of ideals $ {S_1} \triangleleft \cdots \triangleleft {S_t} = S$ such that $ t \leq {2^{n + 1}}$ and any Rees factor semigroup $ {S_i}/{S_{i - 1}}$ is either completely 0-simple or nilpotent of index not exceeding $ \prod _{j = 0}^n(_j^n)$. This sharpens the main result of [4], in particular solving Problem 3.9 from [3].


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0770522-4
PII: S 0002-9939(1985)0770522-4
Article copyright: © Copyright 1985 American Mathematical Society