Commuting Regular Semigroup Rings 1
Yu Xiaofeng, Jiang Shan, Xie Jing-ran · 2009
Strongly regular semigroup rings of non-unitary commutative rings is characterized. It is proved that a commuting regular semigroup is exactly an inflation of a Clifford semigroup and that a commuting regular ring is exactly a direct sum of strongly regular ring with a zero ring. Sufficient and necessary conditions for semigroup rings of commutative rings to be commuting regular are presented.