NDLI: R-bands of r-archimedean ordered semigroups

Content Provider	Springer Nature Link
Author	Kehayopulu, N. Tsingelis, M.
Copyright Year	2009
Abstract	Some semigroups (without order) are decomposable into r-archimedean semigroups. In the present paper we deal with the problem of decomposing certain ordered semigroups into r (l)-archimedean components. The semilattice congruences play an important role in 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. The characterization of complete semilattices of semigroups of a given type has been considered by the same authors. Band congruences play an important role in studying the decomposition of some ordered semigroups, like the decomposition of t-archimedean ordered semigroups. The r (l)-band congruences have been also proved to be useful in studying the decomposition of some types of ordered semigroups, especially the decomposition of r (l)-archimedean ordered semigroups. In this paper we first prove that an ordered semigroup S is an r (resp. l)-band of semigroups of a given type $$ \mathcal{T} $$ if and only if it is decomposable into pairwise disjoint subsemigroups S $_{ α }$ of S of type $$ \mathcal{T} $$ indexed by a band B such that S $_{ α }$ S $_{ β }$ ⊆ S $_{ αβ }$ for all α, β ∈ B and S $_{ α }$ ∩ (S $_{ β }$] ≡ Ø implies α = βα (resp. α = αβ). Thenwe characterize the r (resp. l)-bands of r (resp. l)-archimedean semigroups.
Starting Page	146
Ending Page	153
Page Count	8
File Format	PDF
ISSN	19950802
Journal	Lobachevskii Journal of Mathematics
Volume Number	30
Issue Number	2
e-ISSN	18189962
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2009-06-06
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Ordered semigroup congruence semilattice (complete semilattice) congruence band congruence r-band l-band r (l)-archimedean ordered semigroup r (l)-band of r (l)-archimedean ordered semigroups Ordered semigroups and monoids Probability Theory and Stochastic Processes Mathematical Logic and Foundations Geometry Analysis Algebra Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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