The structure of elements in finite full transformation semigroups


Creative Commons License

AYIK G. , Ayik H. , UNLU Y., HOWIE J.

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, cilt.71, ss.69-74, 2005 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 71 Konu: 1
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1017/s0004972700038028
  • Dergi Adı: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.69-74

Özet

The index and period of an element a of a finite semigroup are the smallest values of m >= 1 and r >= 1 such that a(m+r) = a(m). An element with index m and period 1 is called an m-potent element. For an element a of a finite full transformation semigroup with index m and period r, a unique factorisation alpha = sigma beta such that Shift(sigma) boolean AND Shift(beta) = theta is obtained, where sigma is a permutation of order r and beta is an m-potent. Some applications of this factorisation are given.