右$P$ -可比半群
Right $P$-comparable semigroups
摘要：
本文引入了半群的右腰和右比较理想的概念。特别地，我们研究了含有右腰和右比较子理想的半群的理想理论。我们还研究了右锥的性质，这些性质可以推广到右$P$ -可比半群。给出了半群的幂零元幂零元集是理想的充分和必要条件。我们给出了右理想是右腰的几个等价刻画。在我们的一个主要结果中，我们证明了在具有左消去律的右$P_1$ -可比半群中，素段$P_2\subset P_1$是阿基米德的，简单的或例外的，推广了右锥的一个类似结果到$P$ -可比半群.
英文摘要：
In this paper we introduce the notion of right waist and right comparizer ideals for semigroups. In particular, we study the ideal theory of semigroups containing right waists and right comparizer ideals. We also study those properties of right cones that can be carried over to right $P$-comparable semigroups. We give sufficient and necessary conditions on the set of nilpotent elements of a semigroup to be an ideal. We provide several equivalent characterizations for a right ideal being a right waist. In one of our main result we show that in a right $P_1$-comparable semigroup with left cancellation law, a prime segment $P_2\subset P_1$ is Archimedean, simple or exceptional, extending a similar result of right cones to $P$-comparable semigroups.
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