关于广义纯正断面的一个注记

Earmark on Generalized Orthodox Transversals

讨论了具有广义纯正断面的正则半群及其若干子类的一些代数性质.特别的,证明了以下结论:若分别用RI、RGI、RO、RGO来表示具有逆断面、广义逆断面、纯正断面和广义纯正断面的正则半群类,则有RI?RO,RI?RGI,RO∪RGI?RGO.

This paper has studied some algebraic properties of the class of regular semigroups with generalized orthodox transversals and its several sub-classes.In particular,the following result is obtained:denote the classes of regular semigroups with inverse transversals,generalized inverse transversals,orthodox transversals and generalized orthodox transversals by RI,RGI,RO,RGO,respectively.Then RI?RO,RI?RGI,RO ∪RGI?RGO.