具有可乘适当断面的富足半群

Abundant Semigroups with a Multiplicative Adequate Transversal

研究了一类具有可乘适当断面的富足半群,推广了带有逆断面的正则半群的一个定理.主要结果为:若S0是一个适当半群,幂等元半格为E0,I是一个带有可乘适当断面E0的左正规带,L是一个带有可乘适当断面S0的富足半群,它的幂等元组成一个右正规带.在集合I|×|L上定义一种乘法运算,可以得到I|×|L是一个富足半群,它的可乘适当断面同构于S0.

The aim of this paper is to investigate abundant semigroups with a multiplicative adequate transversal.We give a structure of dual-pair of this semigroup.It derives from the conclusion of a regular semigroup with an inverse transversal.The main theorem is that if S0 is an adequate semigroup,E0 is the idempotent set of S0,I is a left normal band with a multiplicative adequate transversal E0,L is an abundant semigroup with a multiplicative adequate transversal S0 whose idempotents form a right normal band,we define a new operation on the set I|×|L and can get I|×|L is an abundant semigroup whose multiplicative adequate transversal is isomorphic to S0.