| Title: |
On Quasicommutative Ordered Semigroups. |
| Authors: |
Xin-Zhai Xu1 xzhxu8@beelink.com, Yun-Ying Ma1 |
| Source: |
Southeast Asian Bulletin of Mathematics. 2007, Vol. 31 Issue 3, p599-604. 6p. |
| Subject Terms: |
*ABELIAN semigroups, *ORDERED groups, *IDEMPOTENTS, *SEMILATTICES, *INTEGERS, *CONGRUENCE lattices, *LATTICE ordered groups |
| Abstract: |
In this paper, we introduce the concept of quasicommutative ordered semigroups. First we show that the periodic quasicommutative ordered semigroups S in which every idempotent is a minimal element of S is semilattice of quasicommutative ordered semigroups. Then we define a relation η on the quasicommutative ordered semigroup S as follows : aηb if and only if bm ≤ ax, an ≤ by for some x, y ∈ S and some positive integers m, n. We show that the relation η is the least complete semilattice congruence on S and the greatest semilattice congruence on S such that each congruence class is an archimedean ordered subsemigroup. [ABSTRACT FROM AUTHOR] |
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