Tameness of pseudovariety joins involving R

• Type: Article in International Scientific Journal
• Date: 2005

Authors

Almeida, J (Author) FCUP; Costa, JC (Author) Other; Zeitoun, M (Author) Other

Journal

Title: Monatshefte für Mathematik

Vol. 146

Pages: 89-111

ISSN: 0026-9255

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 18 Citations

Scopus - 17 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-16N

DOI: 10.1007/s00605-005-0324-1

Abstract (EN): In this paper, we establish several decidability results for pseudovariety joins of the form V boolean OR W, where V is a subpseudovariety of J or the pseudovariety R. Here, J (resp. R) denotes the pseudovariety of all J-trivial ( resp. R-trivial) semigroups. In particular, we show that the pseudovariety V boolean OR W is ( completely) kappa-tame when V is a subpseudovariety of J with decidable kappa-word problem and W is ( completely) kappa-tame. Moreover, if W is a kappa-tame pseudovariety which satisfies the pseudoidentity x(1) ... x(r)y(omega+1)zt(omega) = x(1) ... x(r)yzt(omega), then we prove that R boolean OR W is also kappa-tame. In particular the joins R boolean OR Ab, R boolean OR G, R boolean OR OCR, and R boolean OR CR are decidable.

Language: English

Type (Professor's evaluation): Scientific