Iteration of expansions - unambiguous semigroups

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

New expansions for global semigroup theory are developed. Many expansions have a left and a right version, each with specific (dual) properties; e.g., the Rhodes expansions ŜL, resp. ŜR, have unambiguous L-resp. R-order. In applications one sometimes needs expansions having both properties simultaneously; these can be constructed by alternately applying the left and the right expansion (possibly infinitely often) while keeping the same set of generators. Thus one obtains an expansion which is invariant under application of the old two expansions and thus has the properties of both (e.g., one obtains -+ with {A figure is presented}, and so -+ has unambiguous L-and R-order). It is proved that, in the case of the Rhodes expansion, the new expansion is 'close' to the original semigroup; in particular (and this is the main result of the paper), Ŝ+A is finite (resp. finite J-above) if S is finite (resp. finiteJ-above).

Original languageEnglish (US)
Pages (from-to)1-55
Number of pages55
JournalJournal of Pure and Applied Algebra
Volume34
Issue number1
DOIs
StatePublished - Jan 1 1984

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Semigroup
Iteration
Semigroup Theory
Figure
Generator
Invariant

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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title = "Iteration of expansions - unambiguous semigroups",
abstract = "New expansions for global semigroup theory are developed. Many expansions have a left and a right version, each with specific (dual) properties; e.g., the Rhodes expansions ŜL, resp. ŜR, have unambiguous L-resp. R-order. In applications one sometimes needs expansions having both properties simultaneously; these can be constructed by alternately applying the left and the right expansion (possibly infinitely often) while keeping the same set of generators. Thus one obtains an expansion which is invariant under application of the old two expansions and thus has the properties of both (e.g., one obtains -+ with {A figure is presented}, and so -+ has unambiguous L-and R-order). It is proved that, in the case of the Rhodes expansion, the new expansion is 'close' to the original semigroup; in particular (and this is the main result of the paper), Ŝ+A is finite (resp. finite J-above) if S is finite (resp. finiteJ-above).",
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Iteration of expansions - unambiguous semigroups. / Birget, Jean-Camille.

In: Journal of Pure and Applied Algebra, Vol. 34, No. 1, 01.01.1984, p. 1-55.

Research output: Contribution to journalArticle

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N2 - New expansions for global semigroup theory are developed. Many expansions have a left and a right version, each with specific (dual) properties; e.g., the Rhodes expansions ŜL, resp. ŜR, have unambiguous L-resp. R-order. In applications one sometimes needs expansions having both properties simultaneously; these can be constructed by alternately applying the left and the right expansion (possibly infinitely often) while keeping the same set of generators. Thus one obtains an expansion which is invariant under application of the old two expansions and thus has the properties of both (e.g., one obtains -+ with {A figure is presented}, and so -+ has unambiguous L-and R-order). It is proved that, in the case of the Rhodes expansion, the new expansion is 'close' to the original semigroup; in particular (and this is the main result of the paper), Ŝ+A is finite (resp. finite J-above) if S is finite (resp. finiteJ-above).

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