关于完全正则和Clifford序半群
On completely regular and Clifford ordered semigroups
摘要：
Lee和Kwon [12]定义了一个序半群S是完全正则的，如果对任意a2 S，a2（a2 Sa 2].刻画了完全正则序半群为t-单子半群的并，Clifford序半群为t-单子半群的完备半格.建立了完全正则序半群的格林定理。在一个序半群S中，我们称一个元素e为序幂等元，如果它满足e？e2.利用序幂等元对正则、完全正则和Clifford序半群进行了不同的刻画。从而发展了完全正则序半群和Clifford序半群的基础
英文摘要：
Lee and Kwon [12] defined an ordered semigroup S to be completely regular if a 2 (a2Sa2] for every a 2 S. We characterize every completely regular ordered semigroup as a union of t-simple subsemigroups, and every Clifford ordered semigroup as a complete semilattice of t-simple subsemigroups. Green's Theorem for the completely regular ordered semigroups has been established. In an ordered semigroup S, we call an element e an ordered idempotent if it satisfies e ? e2. Different characterizations of the regular, completely regular and Clifford ordered semigroups are done by their ordered idempotents. Thus a foundation for the completely regular ordered semigroups and Clifford ordered semigroups has been developed
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