Analysis reveals conditions for semigroup rings to be semiboolean in regular semigroups, suggesting novel criteria for unique cleanliness.
The semibooleanness is a clean property of rings. The aim of this paper is to determine when a semigroup ring is semiboolean. The conditions on a coefficient ring together with conditions on a [Formula: see text]-semigroup (regular semigroup) are completely characterized when the corresponding semigroup ring is semiboolean. Moreover, we give criteria for a regular semigroup ring to be uniquely clean.
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Guo et al. (2025) studied this question.
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