Isomorphish theorems for variants of some semigroups
Ruanglak Jongchotinon, Sureeporn Chaopraknoi, Yupaporn Kemprasit · 2011
A variant of a semigroup induced by is the semigroup where for all and is denoted by . In this research, it is shown that for if and only if . Let be the semigroup under composition of all linear transformations from a vector space over a field into itself. We show that if is finite-dimensional and is a finite field, then for if and only if . We have a consequence that for if and only if where is the set of all matrices over . In addition, isomorphism theorems for the variants of the following semigroups are studied: multiplicative and additive semigroups of integers, some semigroups of transformations of sets and some other semigroups of linear transformations.