含幺Clifford半群上的Rees矩阵半群的同余和正规加密群结构

给出了含幺Clifford半群上的Rees矩阵半群S的正规加密群结构,证明了在含幺Clifford半群上的Rees矩阵半群S上以下两个条件是等价的:(1)S上的同余ρ是完全单半群同余;(2)S上的同余ρ和S上的相容组之间存在保序双射.最后还证明了S上的完全单半群同余所构成的同余格是半模的.

The Regular Cryptogroup Construction and Congruence of a Rees Matrix Semigroup over a Clifford Semigroup with Identity

We investigate the regular cryptogroup construction of the Rees matrix semigroup over a Clifford semigroup with identity;secondly prove that the two conditions are equivalent on a Rees matrix semigroup S over a Clifford semigroup with identity:(1) the congruenceρof S is a completely simple semigroup congruence;(2) there is an order-preserving bijection from the congruences of S to the admissible triples of S;finally prove that the lattice of completely simple congruences on a Rees semigroup over a Clifford semigroup with identity is semimodular.