A class of unary semigroups admitting a Rees matrix representation

作者：Billhardt B; Giraldes E; Marques Smith P; Martins P Mendes^*

来源：Semigroup Forum, 2013, 87(3): 639-652.

DOI：10.1007/s00233-013-9496-5

• Regular semigroup
• Associate inverse subsemigroup
• Variety
• Completely simple semigroups

In Billhardt et al. (Semigroup Forum 79:101-118, 2009) the authors introduced the notion of an associate inverse subsemigroup of a regular semigroup, extending the concept of an associate subgroup of a regular semigroup, first presented in Blyth et al. (Glasgow Math. J. 36:163-171, 1994). %26lt;br%26gt;The main result of the present paper, Theorem 2.15, establishes that a regular semigroup S with an associate inverse subsemigroup S (au) satisfies three simple identities if and only if it is isomorphic to a generalised Rees matrix semigroup M(T;A,B;P), where T is a Clifford semigroup, A and B are bands, with common associate inverse subsemigroup E(T) satisfying the referred identities, and P is a sandwich matrix satisfying some natural conditions. %26lt;br%26gt;If T is a group and A, B are left and right zero semigroups, respectively, then the structure described provides a usual Rees matrix semigroup with normalised sandwich matrix, thus generalising the Rees matrix representation for completely simple semigroups.

• 出版日期2013-12