拟Clifford半环的性质与结构

STRUCTURE AND CHARACTERIZATIONSOF QUASI-CLIFFORD SEMIRINGS

为了进一步研究加法半群为纯整群的半环,在左Clifford半环、矩形Clifford半环的延伸下,得出了一种新的半环,将它定义为拟Clifford半环.一个半环S称为拟Clifford半环,若S是矩形环Sα的分配格D(α∈D),并且E+(S)是一个正则带.同时结合拟Clifford半群的定义和性质,研究得出拟Clifford半环S的加法半群(S,+)为拟Clifford半群,并且给出了拟Clifford半环的具体性质和一个半环为拟Clifford半环的充分必要条件,最后在拟Clifford半群织积结构的前提下,得出了拟Clifford半环的织积结构.

In order to further study the semirings whose additive semigroups are orhogroup.Under the extension of the left-Clifford semiring and the rectanglar-Clifford,a new semiring was obtained,which was defined as the quasi-Clifford semiring.A semiring S is called quasi-Clifford semiring,if S is a distribture lattice of a rectanglar ring Sα(α∈D)and E+(S)is a regular band.At the same time,combined with the structure of the quasi-Clifford semigroup,it was studied that the additive semigroup of the quasi Clifford semiring is the quasi-Clifford semigroup,and gives the sufficient and necessary conditions for a ring to be a quasi-Clifford semiring.Finally,on the premise of the spined product structure of quasi-semigroup,the spined product structure of quasi-Clifford semiring was obtained.