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Original Articles

On the Finite and Nonfinite Generation of Diagonal Acts

Pages 3123-3137 | Received 15 Apr 2005, Published online: 23 Nov 2006
 

Abstract

The diagonal right act of a semigroup S is the set S × S, with S acting by componentwise multiplication from the right. The diagonal left act and diagonal bi-act of S are defined analogously.

Necessary and sufficient conditions are found for the finite generation of the diagonal bi-acts of completely zero-simple semigroups and completely simple semigroups. It is also proved that various classes of semigroups do not have finitely generated or cyclic diagonal right, left, or bi-acts.

Notes

Communicated by V. Gould.

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