S-系的Goldie扭类

GOLDIE TORSION CLASSES OF S-SYSTEMS

本文对有0,1的半群S,利用S-系的奇异性建立了S-系的Goldie扭论(?),并且得到相应于(?)的扭自由类是由全体非奇异S-系构成。我们证明了,Goldie扭论是特殊扭论的充要条件是S的任意本质右同余都包含一个由(?)-本质右理想确定的Rees同余。

Let S be a semigroup with 0 and 1. Using singularity of S-systems we established Goldie torsion theory τ_G of S-systems, and proved that the class of all nonsingular right S-systems is a torsion free class of τ_G. We obtained τ_G is special if and only if there exists a η-essential right ideal Ⅰ such that (Ⅰ×Ⅰ)∪0(?)ρ for each essential right congruence ρ of S.