Stability and J-depth of expansions

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Abstract

In this paper I prove that if a semigroup S is stable then [formula omitted] L(S) and [formula omitted] R(S) (the Rhodes expansions), and [formula omitted]+(SA) (the iteration of those expansions) are also stable. I also prove that if S is stable and has a J-depth function then these expansions also have a J-depth functon. More generally, if X →→ S is a J*-surmorphism and if S is stable and has a J-depth function then X has a J-depth function. All these results are needed for the structure theory of semigroups which are stable and have a J-depth function. The techniques used were originally developed by the author to prove that [formula omitted]+(SA) is finite if S is finite (later Rhodes found a much more direct proof of that result).

Original languageEnglish (US)
Pages (from-to)41-54
Number of pages14
JournalBulletin of the Australian Mathematical Society
Volume38
Issue number1
DOIs
StatePublished - Aug 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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