Structure of Strict Abundant Semigroups
Yizhi Chen, Bo Yang, Aiping Gan · Algebra Colloquium · 2019
We introduce a new class of semigroups called strict abundant semigroups, which are concordant semigroups and subdirect products of completely [Formula: see text]-simple abundant semigroups and completely 0-[Formula: see text]-simple primitive abundant semigroups. A general construction and a tree structure of such semigroups are established. Consequently, the corresponding structure theorems for strict regular semigroups given by Auinger in 1992 and by Grillet in 1995 are generalized and extended. Finally, an example of strict abundant semigroups is also given.