Strongly 𝜋-regular matrix semigroups

Okniński, Jan

doi:10.1090/S0002-9939-1985-0770522-4

Strongly $\pi$-regular matrix semigroups
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Proc. Amer. Math. Soc. 93 (1985), 215-217 Request permission

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].

References

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On regular semigroup rings