On weak commutativity of po-semigroups and their semilattice decompositions |
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Authors: | Yonglin Cao |
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Institution: | 1. Department of Mathematics, Zibo Normal College, Zibo, Shandong, 255013, P.R.China
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Abstract: | In this paper, concepts of left (right) weakly commutative po-semigroups and r (l or t)-archimedean subsemigroups of a po-semigroup are introduced. Six relations τ, σ, η, ρ, μ, ξ on a po-semigroup are defined. By using them, filters and radicals, fourteen necessary and sufficient conditions in order that a po-semigroup is a semilattice of archimedean subsemigroups are given. The facts that a left weakly commutative (right weakly commutative or weakly commutative) po-semigroup is a semilattice of r (l or t) -archimedean subsemigroups are proved and seven characterizations of these po-semigroups are obtained respectively. |
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