Minimal presentations and efficiency of semigroups

Ayik H., CAMPBELL C., O'CONNOR J., RUSKUC N.

SEMIGROUP FORUM, cilt.60, sa.2, ss.231-242, 2000 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 60 Sayı: 2
  • Basım Tarihi: 2000
  • Dergi Adı: SEMIGROUP FORUM
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.231-242
  • Çukurova Üniversitesi Adresli: Evet

Özet

A finite semigroup S is said to be efficient if it can be defined by a presentation [A \ R] with \R\ - \A\ = rank(H-2(S)). In this paper we demonstrate certain infinite classes of both efficient and inefficient semigroups. Thus, finite abelian groups, dihedral groups D-2n with n even, and finite rectangular bands are efficient semigroups. By way of contrast we show that finite zero semigroups and free semilattices are never efficient. These results are compared with some well-known results on the efficiency of groups.