Minimum Strong P-congruences Determined by Hyper Trace on P-inversive Semigroups
Fan Xing-kui · Journal of Sichuan Normal University · 2012
The class of P-inversive semigroups is a very important one,which is closely linked with the well-known class of regular semigroups.The structures and congruences about P-inversive semigroups are widely studied by numerous domestic and international semigroup workers.In this paper,we study a class of tiny congruences in the strong P-congruence lattices of P-regular semigroups.The concepts of characteristic subsemigroups and hyper traces are introduced and the strong P-congruence on P-inversive semigroups S(P) is investigated in terms of congruence theory.The minimum strong P-congruence whose hyper trace coincide with the hyper trace of given congruence is described and a specific description is presented.These results generalize the corresponding results for regular semigroups.