On the Multiplicative Quasi-Adequate Transversals of an Abundant Semigroup
Xiangfei Ni, Yanfeng Luo · Communications in Algebra · 2010
In this article, we explore the multiplicative quasi-adequate transversals of an abundant semigroup. Let S be an abundant semigroup with multiplicative quasi-adequate transversals. Then the product of any two multiplicative quasi-adequate transversals is also a multiplicative quasi-adequate transversal. Moreover, all multiplicative quasi-adequate transversals of S form a rectangular band. Let S°and S ♭ be multiplicative quasi-adequate transversals of S, and let δ°(δ♭) be the δ-relation on S°(S ♭). Then there exists a bijection ϕ from S°/δ°onto S ♭/δ♭. In particular, if δ°and δ♭ are congruences, then the bijection ϕ is an isomorphism.