Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2014.54.1.123
Title & Authors
Pure Ideals in Ordered Semigroups Changphas, Thawhat; Sanborisoot, Jatuporn;
In this paper the concepts of pure ideals, weakly pure ideals and purely prime ideals in ordered semigroups are introduced. We obtain some characterizations of pure ideals and prove that the set of all pure prime ideals is topologized.
ordered semigroup;weakly regular ordered semigroup;pure ideal;weakly pure ideal;purely prime ideal;topology;
J. Ahsan, M. Takahashi, Pure spectrum of a monoid with zero, Kobe J. Mathematics, 6(1989), 163-182.
G. Birkhoff, Lattice Theory, Providence (1969).
S. Bashir, M. Shabir, Pure ideals in ternary semigroups, Quasigroups and Related Systems, 17(2009), 149-160.
N. Kehayopulu, On weakly prime ideals of ordered semigroups, Mathematica Japonica, 35(6)(1990), 1051-1056.
N. Kehayopulu, M. Tsingelis, On left regular ordered semigroups, Southeast Asian Bulletin of Mathematics, 25(2002), 609-615.
M. Petrich, Introduction to Semigroups, Merrill Columbus (1973).