Characterizing cryptogroups with a finite number of $${\mathcal{H}}$$ -classes in each $${\mathcal{D}}$$ -class by their subsemigroups |
| |
Authors: | Mario Petrich |
| |
Institution: | (1) 21420 Bol, Brač, Croatia |
| |
Abstract: | We construct a family of completely regular semigroups with the property that each completely regular semigroup S with a finite number of -classes in each -class is non-cryptic if and only if S contains an isomorphic image of a member of . Each member F of is an ideal extension of a Rees matrix semigroup J by a cyclic group B with a zero adjoined and the identity of B is the identity of F. Here with I and Λ finite, G is given by generators and relations, and P is given explicitly. Within completely regular semigroups, the cryptic property is equivalent to where is the natural partial order and a
if and only if a
2 = ab = ba. Hence the above result can be formulated in terms of and .
|
| |
Keywords: | Completely regular semigroup Cryptic Cryptogroup Natural partial order Rees matrix semigroup Ideal extension |
本文献已被 SpringerLink 等数据库收录! |