摘要
本文首先定义了交换剩余幺半群Ｍ相对于其子半群Ｐ（Ｍ）的商结构Ｍ／Ｐ（Ｍ），然后研究了它的性质并给出了一些同构定理．证明了Ｍ／Ｐ（Ｍ）仍是一个可换剩余幺半群且Ｍ／Ｐ（Ｍ）≌ＳＰ（Ｍ），其中ＳＰ（Ｍ）＝｛ｘ｜ｘ∈Ｍ，１：（１：ｘ）＝ｘ｝；特别地，当Ｍ具有条件１：（１：ｘ）＝１：ｘ时，Ｍ／Ｐ（Ｍ）≌Ａ（Ｍ），且满足Ｇ：Ｃｘ＝Ｃｘ，逆也成立。
This paper has firstly defined the factor struture M/P(M) of commutatiuely residual monoid M by its sub-monoid P(M), then we have studied its properties and given out some isomorphism theorem. At the same time we have proved that M/P(M) is also a Oumutatiaely residual monoid and M/P(M) ≌ SP(M), here, SP(M)= {x | x∈ M, 1: (1: x)=1: x}. Specially, when M satisfies the condition 1: (1: x) = 1: x, we have M/P(M) ≌ A (M) and M/P (M) satisfies the condition C1=Cx= Cx. The converse is also hold.
出处
《纯粹数学与应用数学》
CSCD
1995年第1期109-113,共5页
Pure and Applied Mathematics
