Sublattices of the Lattices of Strong P-Congruences on P-Inversive Semigroups |
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Authors: | Zenghui Gao Bingjun Yu |
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Institution: | (1) Department of Computation Science, Chengdu University of Information Technology, Chengdu, Sichuan 610225, P.R. China;(2) College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P.R. China |
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Abstract: | In this paper, we describe strong P-congruences and sublattice-structure of the strong P-congruence lattice CP(S) of a P-inversive semigroup S(P). It is proved that the set of all strong P-congruences CP(S) on S(P) is a complete lattice. A close link is discovered between the class of P-inversive semigroups and the well-known class of regular ⋆-semigroups. Further, we introduce concepts of strong normal partition/equivalence,
C-trace/kernel and discuss some sublattices of CP(S). It is proved that the set of strong P-congruences, which have C-traces (C-kernels) equal to a given strong normal equivalence of P (C-kernel), is a complete sublattice
of CP(S). It is also proved that the sublattices determined by C-trace-equaling relation θ and C-kernel-equaling relation κ, respectively,
are complete sublattices of CP(S) and the greatest elements of these sublattices are given. |
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