Band congruences in ordered semigroups

N. Kehayopulu, M. Tsingelis
2007 International Mathematical Forum  
The semilattice congruences play an important role in studying the decomposition of semigroups -without order. When we pass from semigroups without order to ordered semigroups, the same role is played by the complete semilattice congruences. So, the complete semilattice congruences play an essential role in studying the structure, especially the decomposition of ordered semigroups. The characterization of complete semilattices of semigroups of a given type has been already considered by the
more » ... nsidered by the same authors. Band congruences have been also proved to be useful in studying the decomposition of some types of ordered semigroups, especially the decomposition of t-archimedean ordered semigroups. In this paper we prove that an ordered semigroup S is a band of semigroups of a given type T if and only if it is decomposable into pairwise disjoint subsemigroups S α of S of type T indexed by a band B, such that S α S β ⊆ S αβ for all α, β ∈ B and S α ∩ (S β ] = ∅ implies α = αβ = βα. Mathematics Subject Classification: 06F05
doi:10.12988/imf.2007.07102 fatcat:2pyeuk63jzhqvps6n54wurvptm