Pointed principally ordered regular semigroups
Discussiones Mathematicae General Algebra and Applications (2016)
- Volume: 36, Issue: 1, page 101-111
- ISSN: 1509-9415
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topT.S. Blyth, and G.A. Pinto. "Pointed principally ordered regular semigroups." Discussiones Mathematicae General Algebra and Applications 36.1 (2016): 101-111. <http://eudml.org/doc/286882>.
@article{T2016,
abstract = {An ordered semigroup S is said to be principally ordered if, for every x ∈ S there exists x* = max\{y ∈ S | xyx ⩽ x\}. Here we investigate those principally ordered regular semigroups that are pointed in the sense that the classes modulo Green's relations ℒ,ℛ,𝒟 have biggest elements which are idempotent. Such a semigroup is necessarily a semiband. In particular we describe the subalgebra of (S;*) generated by a pair of comparable idempotents that are 𝒟-related. We also prove that those 𝒟-classes which are subsemigroups are ordered rectangular bands.},
author = {T.S. Blyth, G.A. Pinto},
journal = {Discussiones Mathematicae General Algebra and Applications},
keywords = {regular semigroup; principally ordered; naturally ordered; Green's relations},
language = {eng},
number = {1},
pages = {101-111},
title = {Pointed principally ordered regular semigroups},
url = {http://eudml.org/doc/286882},
volume = {36},
year = {2016},
}
TY - JOUR
AU - T.S. Blyth
AU - G.A. Pinto
TI - Pointed principally ordered regular semigroups
JO - Discussiones Mathematicae General Algebra and Applications
PY - 2016
VL - 36
IS - 1
SP - 101
EP - 111
AB - An ordered semigroup S is said to be principally ordered if, for every x ∈ S there exists x* = max{y ∈ S | xyx ⩽ x}. Here we investigate those principally ordered regular semigroups that are pointed in the sense that the classes modulo Green's relations ℒ,ℛ,𝒟 have biggest elements which are idempotent. Such a semigroup is necessarily a semiband. In particular we describe the subalgebra of (S;*) generated by a pair of comparable idempotents that are 𝒟-related. We also prove that those 𝒟-classes which are subsemigroups are ordered rectangular bands.
LA - eng
KW - regular semigroup; principally ordered; naturally ordered; Green's relations
UR - http://eudml.org/doc/286882
ER -
References
top- [1] T.S. Blyth, Lattices and Ordered Algebraic Structures (Springer, 2005). doi: 10.1007/b139095 Zbl1073.06001
- [2] T.S. Blyth and M.F. Janowitz, Residuation Theory (Pergamon, 1972).
- [3] T.S. Blyth and G.A. Pinto, Principally ordered regular semigroups, Glasgow Math. J. 32 (1990), 349-364. doi: 10.1017/S0017089500009435 Zbl0725.06008
- [4] T.S. Blyth and G.A. Pinto, Idempotents in principally ordered regular semigroups, Communications in Algebra 19 (1991), 1549-1563. doi: 10.1080/00927879108824220 Zbl0728.06010
- [5] T.S. Blyth and M.H. Almeida Santos, On weakly multiplicative inverse transversals, Proc. Edinburgh Math. Soc. 37 (1993), 93-99. doi: 10.1017/S001309150001871X Zbl0819.20068
- [6] P.M. Higgins, Techniques of Semigroup Theory (Oxford Science Publiications, 1992). doi: 10.1007/BF02573500
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