Fixed Points of Endomorphisms and Metrics in preGarside Monoids
| Autor: | Oussama Ajbal |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Monoid
Algebra and Number Theory Endomorphism Trace (linear algebra) Mathematics::Rings and Algebras 010102 general mathematics 0102 computer and information sciences Fixed point Trace monoid 01 natural sciences Combinatorics Mathematics::Group Theory 010201 computation theory & mathematics Mathematics::Category Theory Finitely-generated abelian group 0101 mathematics Computer Science::Formal Languages and Automata Theory Mathematics |
| Zdroj: | Communications in Algebra. 44:2685-2706 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2015.1065842 |
| Popis: | E. Rodaro and P. V. Silva proved recently that the fixed points submonoid and the periodic points submonoid of a trace monoid endomorphism are always finitely generated. We show that for finitely generated left preGarside monoids, the fixed and periodic points submonoids of any endomorphism are also finitely generated left preGarside monoids under some condition, and in the particular case of Artin–Tits monoids, these submonoids are Artin–Tits monoids too. We prove algebraically some inequalities, equivalences, and nonequivalences between three metrics in finitely generated preGarside monoids, and especially in trace monoids and Garside monoids. |
| Databáze: | OpenAIRE |
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