On finiteness conditions for Rees matrix semigroups

Creative Commons License

Ayik H.

CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.55, no.2, pp.455-463, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 2
  • Publication Date: 2005
  • Doi Number: 10.1007/s10587-005-0035-8
  • Journal Name: CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.455-463
  • Çukurova University Affiliated: Yes

Abstract

Let T = M[S; I, J; P] be a Rees matrix semigroup where S is a semigroup, I and J are index sets, and P is a J x I matrix with entries from S, and let U be the ideal generated by all the entries of P. If U has finite index in S, then we prove that T is periodic (locally finite) if and only if S is periodic (locally finite). Moreover, residual finiteness and having solvable word problem are investigated.