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Finiteness conditions for matrix semigroups


Author: Yechezkel Zalcstein
Journal: Proc. Amer. Math. Soc. 38 (1973), 247-249
DOI: https://doi.org/10.1090/S0002-9939-1973-0310094-3
MathSciNet review: 0310094
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Abstract | References | Additional Information

Abstract: Classical theorems of Schur and Burnside on finiteness of matrix groups are generalized to regular and inverse matrix semigroups.


References [Enhancements On Off] (What's this?)

  • [1] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vols. 1, 2, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R.I., 1961, 1967. MR 24 #A2627; MR 36 #1558.
  • [2] M. Coudrain et M. P. Schützenberger, Une condition de finitude des monoïdes finiment engendrés, C.R. Acad. Sci. Paris Sér. A-B 262 (1966), A1149-A1151. MR 33 #2742. MR 0194532 (33:2742)
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  • [4] Y. Zalcstein, Studies in the representation theory of finite semigroups, Trans. Amer. Math. Soc. 161 (1971), 71-87. MR 0283104 (44:337)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310094-3
Keywords: Matrix semigroup, Schur theorem, d.c.c. on principal ideals
Article copyright: © Copyright 1973 American Mathematical Society

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