Green index and finiteness conditions for semigroups
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Let S be a semigroup and let T be a subsemigroup of S. Then T acts on S by left and by right multiplication. If the complement S \ T has finitely many strong orbits by both these actions we say that T has finite Green index in S. This notion of finite index encompasses subgroups of finite index in groups, and also subsemigroups of finite Rees index (complement). Therefore, the question of S and T inheriting various finiteness conditions from each other arises. In this paper we consider and resolve this question for the following finiteness conditions: finiteness, residual finiteness, local finiteness, periodicity, having finitely many right ideals, and having finitely many idempotents. (c) 2008 Elsevier Inc. All rights reserved.
Gray , R D & Ruskuc , N 2008 , ' Green index and finiteness conditions for semigroups ' Journal of Algebra , vol 320 , no. 8 , pp. 3145-3164 . , 10.1016/j.jalgebra.2008.07.008
Journal of Algebra
This is an author version of this article. The published version (c) 2008 Elsevier Inc. is available at www.sciencedirect.com
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