An equivalence in a selected family of cyclic subsemigroups and algorithm for generating systems of semigroup

الملخص

This paper focuses on generators of cyclic subsets of semigroups which determines the whole semigroup through algebraic closure. We call a generating set minimal if it does not have a proper generating subset. A set is independent if no element of the set can be generated by the remaining members of the set. Independent subsystems of cyclic semigroups are intersected to obtain the generating set of cyclic semigroups. From intersecting subsystems of cyclic semigroups, a certain equivalence relation on the set of all cyclic Subsemigroups are obtained. The paper also shows how such equivalence relation is a tool for partitioning cyclic subsemigroups into generating subsystems. Algorithm to find the minimal generating set of a semigroups is given.