正则半群上的I－同余

THE I-CONGRUENCES ON A REGULAR SEMIGROUP

设Ｓ是正则半群，ＣｏｎＳ表示Ｓ上所有同余的集合，对ρ；σ∈ＣｏｎＳ，本文给出了ρ是Ｓ上Ｉ—同余的几个等价条件，以及当ρ，σ是Ｉ—同余时，ρ∧σ和ρ∨σ是Ｉ—同余的充要条件．

Let S be a regular semigroup and ConS be the set of all congruences on S. For ρ,∈ConS, this paper gives a few equivalent conditions that ρ is an I-congruence on S,and a necessary and sufficient condition which ρ∧σ and ρ∨σare I-congruenes on S respectively if ρ and σ are the I-congruences on S.