完全単純半群の半束であるような半群の正則拡大について

The structure of orthodox semigroups was described by Hall [2], Warne [4], [5] and the author L7], [8], [9] in terms of bands and inverse semigroups. In this paper, we introduce the concept of generalized orthodox semigroups and show that some analogues to the results given by the papers above for the class of orthodox semigroups are also fulfilled by the class of generalized orthodox semigroups. Further, we completely describe the structure of generalized orthodox semigroups in terms of Cliffordian semigroups (that is, semlgroups which are unions of groups) and inverse semigroups. In the latter half of the paper, we introduce the concept of split extensions of Cliffordran semigroups by inverse semigroups, and next establish some necessary and sufficient conditions in order that a regular semigroup S be a split extension of a normal Cliffordian subsemigroup of S by an inverse semigroup. Any notation and terminology should be referred to [1], unless otherwrse stated.