整体决定的一类Clifford半群(英文)

A Class of Globally Determined Clifford Semigroups

如果半格E中的一个元素不能表示为E中两个都不同于它自身的元素的乘积,则称该元素为E中的素元.本文将证明其半格可由素元生成的这类Clifford半群是整体决定的.这一结论推广了Gould和Ⅰskra,于1984年发表在《Semigroup Forum》上的一个结果.

An element of a semilattice is called prime （in terms of lattice, ＂meet irre- ducible＂） if it cannot be expressed as a product of two elements distinct from itself. In this paper we show that the class of Clifford semigroups whose semilattices are generated by their prime elements is globally determined. This extends the result given by Gould and Iskra in Semigroup Forum in 1984.