| Autor: |
Deluca, A., Varricchio, S. |
| Zdroj: |
Advances in Mathematics; September 1994, Vol. 108 Issue: 1 p91-103, 13p |
| Abstrakt: |
Let Sbe a semigroup. For s, t∈ Swe set s≤Btif s∈ {t} ∪ tS1t; we say that Ssatisfies the condition minB, if and only if any strictly descending chain w.r.t. ≤Bof elements of Shas a finite length. The main result of the paper is the following theorem: Let T be a semigroup satisfying minB. Let T′ be a subsemigroup of T such that all subgroups of T are locally finite in T′. Then T′ is locally finite. This result is a noteworthy generalization of a theorem of Coudrain and Schützenberger. Moreover, as a corollary we obtain the theorem of McNaughton and Zalcstein which gives a positive answer to the Burnside problem for semigroups of matrices on a field. |
| Databáze: |
Supplemental Index |
| Externí odkaz: |
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