Strongly $\pi$-regular matrix semigroups
HTML articles powered by AMS MathViewer
- by Jan Okniński PDF
- 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
-
N. Bourbaki, Algèbre, Chapitre III, Hermann, Paris, 1948.
- Carl Faith, Algebra. II, Grundlehren der Mathematischen Wissenschaften, No. 191, Springer-Verlag, Berlin-New York, 1976. Ring theory. MR 0427349, DOI 10.1007/978-3-642-65321-6
- Mohan S. Putcha, On linear algebraic semigroups. I, II, Trans. Amer. Math. Soc. 259 (1980), no. 2, 457–469, 471–491. MR 567091, DOI 10.1090/S0002-9947-1980-0567091-0
- Mohan S. Putcha, Matrix semigroups, Proc. Amer. Math. Soc. 88 (1983), no. 3, 386–390. MR 699399, DOI 10.1090/S0002-9939-1983-0699399-0
- Robert McNaughton and Yechezkel Zalcstein, The Burnside problem for semigroups, J. Algebra 34 (1975), 292–299. MR 374301, DOI 10.1016/0021-8693(75)90184-2 J. Okniński, On regular semigroup rings, Proc. Roy. Soc. Edinburgh (to appear).
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 215-217
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770522-4
- MathSciNet review: 770522