Rank properties of certain semigroups

MİNİSKER M.

Semigroup Forum, vol.78, no.1, pp.99-105, 2009 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 78 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1007/s00233-008-9089-x
  • Journal Name: Semigroup Forum
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.99-105
  • Keywords: Free semilattice, Large rank, Small rank
  • Hatay Mustafa Kemal University Affiliated: Yes

Abstract

In this paper we consider certain ranks of some semigroups. These ranks are r 1(S),r 2(S),r 3(S),r 4(S) and r 5(S) as defined below. We have r 1 r 2 r 3 r 4 r 5. The semigroups are CL n ,CL m ×CL n ,Z n and SL n . Here CL n is a chain with n elements, Z n is the zero semigroup on n elements and SL n is the free semilattice generated by n elements and having 2 n -1 elements. We find many of the ranks for these classes of semigroups. © 2008 Springer Science+Business Media, LLC.