关于右单纯右可消的半群

设S是一个右单纯、右可消的半群。本文讨论了S中方程ax=b的解集合的基数,证明了:对于S中任意的元素a、b、c和d,方程ax=b与cx=d的解集合有相同的基数。并且S成群的一个充分必要条件是S中存在一对元素a与b,使方程ax=b在S中只有有限个解.

ON RIGHT SIMPLE RIGHT CANCELLATIVE SEMIGROUPE

Let S be a right simple right cancellative semigroup. In this paper, the cardinal number of the solution set of an equation ax =b in S is studied. We proved: For any a, b, c, d in S, the solution sets of ax=b and cx=d have the same cardinality. And S is a group if there is a pair of elements a and b of S such that the eqution ax =b has only finite solutions.