含正则*-断面的正则半群(英文)

Regular Semigroups with Regular *-Transversals

首先给出了含正则*断面的正则半群类的一些新性质,然后证明了正则半群的左(右)理想正则*断面是其强正则*断面.根据这些性质,通过两个含共同的强正则*断面S°的半群L和R以及相关映射给出了含拟理想正则*断面的正则半群类的一个新的结构定理,其中S°是L的左理想,是R的右理想.

Some new properties of regular semigroups with regular ＊-transversals are given. In particular, it is proved that a right （or left） ideal regular ＊ -transversals of a regular semigroup S is a strongly regular ＊ -transversals of S. According to these new properties, it is given that a new structure for regular semigroups with quasi-ideal regular ＊ -transversals by two regular semigroups R and L with a common strongly regular ＊ -transversals S^o such that S^o is a right ideal and a left ideal of R and L, respectively.