### 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]+(S_{A}) (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]+(S_{A}) is finite if S is finite (later Rhodes found a much more direct proof of that result).

Original language | English (US) |
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Pages (from-to) | 41-54 |

Number of pages | 14 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 38 |

Issue number | 1 |

DOIs | |

State | Published - Aug 1988 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)