Equational theories of semigroups with involution / Auinger Karl,Dolinka Igor,Volkov Mikhail V. // JOURNAL OF ALGEBRA. - 2012. - V. 369, l. . - P. 203-225.

ISSN/EISSN:

0021-8693 / нет данных

Type:

Article

Abstract:

We employ the techniques developed in an earlier paper to show that involutory semigroups arising in various contexts do not have a finite basis for their identities. Among these are partition semigroups endowed with their natural inverse involution, including the full partition semigroup C-n for n >= 2, the Brauer semigroup B-n for n >= 4 and the annular semigroup B-n for n >= 4, n even or a prime power. Also, all of these semigroups, as well as the Jones semigroup J(n) for n >= 4, turn out to be inherently nonfinitely based when equipped with another involution, the `skew' one. Finally, we show that similar techniques apply to the finite basis problem for existence varieties of locally inverse semigroups. (c) 2012 Elsevier Inc. All rights reserved.

Author keywords:

(Non)finitely based algebraic structure; Involutory semigroup; Partition semigroup; Existence variety EXISTENCE VARIETIES; PARTITION ALGEBRAS; REGULAR-SEMIGROUPS; IDENTITIES; LATTICE; BASES

DOI:

10.1016/j.jalgebra.2012.06.021

Web of Science ID:

ISI:000308448700010

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	NOV 1
Publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE
Address	525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Language	English
Keywords-Plus	EXISTENCE VARIETIES; PARTITION ALGEBRAS; REGULAR-SEMIGROUPS; IDENTITIES; LATTICE; BASES
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics
Author-Email	karl.auinger@univie.ac.at dockie@dmi.uns.ac.rs mikhail.volkov@usu.ru
ResearcherID-Numbers	Volkov, Mikhail/F-1407-2014
ORCID-Numbers	Volkov, Mikhail/0000-0002-9327-243X Dolinka, Igor/0000-0002-8644-0626
Funding-Acknowledgement	Ministry of Education and Science of the Republic of Serbia {[}174019]; Secretariat of Science and Technological Development of the Autonomous Province of Vojvodina {[}114-451-2002/2011]; Russian Foundation for Basic Research {[}10-01-00524]
Funding-Text	The second author was supported by Grant No. 174019 of the Ministry of Education and Science of the Republic of Serbia, and by a grant (Contract 114-451-2002/2011) of the Secretariat of Science and Technological Development of the Autonomous Province of Vojvodina. The third author acknowledges support from the Russian Foundation for Basic Research, grant 10-01-00524.
Number-of-Cited-References	45
Usage-Count-Since-2013	1
Journal-ISO	J. Algebra
Doc-Delivery-Number	001GN