具有左中心幂等元的完美l-ample半群

Perfect l-ample semigroups with left central idempotents

定义完美l-ample半群,并研究具有左中心幂等元的完美l-ample半群的半格分解。利用半格分解,证明了半群S为具有左中心幂等元的完美l-ample半群,当且仅当S为直积Mα×Λα的强半格,其中Mα是右可消幂幺半群,Λα是右零带。这一结果为具有左中心幂等元的完美l-ample半群结构的建立奠定了基础。

The concept of perfect 1-ample semigroups is introduced and the semilattice decomposition of perfect 1-ample semigroups with left central idempotents is studied. By using this semilattice decomposition, it is proved that a semigroup S is a perfect 1-ample semigroup with left central idempotents if and only if it is a strong semilattice of a direct product Mα×Λα, where Mα is a right cancellative unipotent monoid and Λα is a right zero band. This result is the basis that the structure theorem of perfect 1-ample semigroups with left central idempotents can be established.