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A characterization of the semigroup of matrix units

Published online by Cambridge University Press:  09 April 2009

Bernard R. Gelbaum  and
Stephen Schanuel
Bernard R. Gelbaum
Affiliation:
Department of Mathematics SUNY/Buffalo, U.S.A.
Stephen Schanuel
Affiliation:
Department of Mathematics SUNY/Buffalo, U.S.A.
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Abstract

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Let I be a set and let (I) denote the set consisting of the 0 matrix over I × I and the matrix units over I × I. Then for x, z in (I) and x≠0≠z, xyz≠0 has precisely one solution y. This and several other statements are shown to be equivalent characterizations of (I) regarded as a semigroup with zero.

1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.

Keywords

Semigroups with zeromatrix unitscategorical semigroups.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 3 , May 1980 , pp. 291 - 296
Copyright
Copyright © Australian Mathematical Society 1980