อันดับบางส่วนธรรมชาติบนกึ่งกรุปการแปลงแบร์-เลวี

Abstract

In this research we study the natural partial order on Baer-Levi semigroup and partial Baer-Levi semigroup with restricted range . We provide necessary and sufficient conditions when any two elements in these semigroups are related under the natural partial order. We also characterize maximal, minimal, maximum and minimum elements including describe the least upper bound and the greatest lower bound. Moreover, an upper cover and a lower cover of each element in these two semigroups are described. Some partial results obtained in this research cover and extend the results which has been published on partial Baer-Levi semigroup .