RELATIVELY INHERENTLY NONFINITELY Q-BASED SEMIGROUPS / Jackson Marcel,Volkov Mikhail // TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - 2009. - V. 361, l. 4. - P. 2181-2206.

ISSN/EISSN:

0002-9947 / нет данных

Type:

Article

Abstract:

We Prove that every semigroup S Whose quasivariety contains a 3-nilpotent semigroup or a semigroup of index more than 2 has no finite basis for its quasi-identities provided that one of the following properties holds: S is finite; S has a faithful representation by injective partial maps on a set; S has a faithful representation by order preserving maps on a chain. As a corollary it is shown that, in an asymptotic sense, almost all finite semi-groups and finite monoids admit no finite basis for their quasi-identities.

Author keywords:

Quasi-identity; quasivariety; universal class; semigroup; injective map; order preserving map; finite q-basis property; inherently nonfinitely q-based semigroup relative to a class; 3-nilpotent semigr ORDER-PRESERVING MAPPINGS; FINITE BASIS PROBLEM; QUASIVARIETIES; ALGEBRAS

DOI:

нет данных

Web of Science ID:

ISI:000263773400022

Соавторы в МНС:

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Другие поля

Поле	Значение
Publisher	AMER MATHEMATICAL SOC
Address	201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA
Language	English
Article-Number	PII S0002-9947(08)04798-3
Keywords-Plus	ORDER-PRESERVING MAPPINGS; FINITE BASIS PROBLEM; QUASIVARIETIES; ALGEBRAS
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics
Author-Email	M.G.Jackson@latrobe.edu.au Mikhail.Volkov@usu.ru
ResearcherID-Numbers	Volkov, Mikhail/F-1407-2014
ORCID-Numbers	Volkov, Mikhail/0000-0002-9327-243X
Funding-Acknowledgement	ARC Discovery Project {[}DP0342459]; Russian Foundation for Basic Research {[}05-01-00540, 06-01-00613]; Institute for Advanced Study of La Trobe University
Funding-Text	The second author acknowledges support from the Russian Foundation for Basic Research, grants 05-01-00540 and 06-01-00613. The paper was initiated during the second author's Distinguished Fellowship at the Institute for Advanced Study of La Trobe University.
Number-of-Cited-References	35
Journal-ISO	Trans. Am. Math. Soc.
Doc-Delivery-Number	413DP