Reducibility vs. definability for pseudovarieties of semigroups

MENESES GUIMARÄES DE ALMEIDA, Jorge Manuel and Ondřej KLÍMA. Reducibility vs. definability for pseudovarieties of semigroups. International Journal of Algebra and Computation. vol. 26, No 7, p. 1483-1495. ISSN 0218-1967. doi:10.1142/S0218196716500648. 2016.

Basic information

• Original name: Reducibility vs. definability for pseudovarieties of semigroups
• Authors: MENESES GUIMARÄES DE ALMEIDA, Jorge Manuel (620 Portugal) and Ondřej KLÍMA (203 Czech Republic, guarantor, belonging to the institution).
• Edition: International Journal of Algebra and Computation, 2016, 0218-1967.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Singapore
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 0.396
• RIV identification code: RIV/00216224:14310/16:00088364
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1142/S0218196716500648
• UT WoS: 000388649200010
• Keywords in English: Pseudovariety; relatively free profinite semigroup; ordered semigroup; completely regular semigroup; commutative semigroup; group
• Tags: AKR, rivok
• Tags: International impact, Reviewed

Abstract

It is easy to show that a pseudovariety which is reducible with respect to an implicit signature sigma for the equation x=y can also be defined by sigma-identities. We present several negative examples for the converse using signatures in which the pseudovarieties are usually defined. An ordered example issue from the extended Straubing–Thérien hierarchy of regular languages is also shown to provide a positive example.

Links

• GA15-02862S, research and development project: Name: Aplikace algebry a kombinatoriky v teorii formálních jazyků

Investor: Czech Science Foundation