Permutative varieties of posemigroups
Shabir Ahmad Ahanger, Aftab Hussain Shah, Noor Mohammad Khan · Communications in Algebra · 2021
We show that the variety of permutative posemigroups is epimorphically closed and all subvarieties of the variety V of permutative posemigroups admitting a permutation identity x1x2⋯xn=xi1xi2⋯xin with in≠n and i2≠2 [i1≠1 and in−1≠n−1] are epimorhically closed. Further, we find certain epimorphically closed subvarieties of the variety V of permutative posemigroups with in≠n [i1≠1]. Finally we show that, under certain conditions, an identity is preserved under posemigroup epis in conjunction with any permutation identity.