TY - JOUR

T1 - Naturally Ordered Orthodox Dubreil-Jacotin Semigroups

AU - Blyth, T. S.

AU - Santos, Maria Helena Coutinho Gomes de Almeida

PY - 1992/1/1

Y1 - 1992/1/1

N2 - The structure of orthodox semigroups with a normal band of idempotents has been described by Yamada. Since, for a naturally ordered strong Dubreil-Jacotin orthodox semigroup, it can be shown that the band of idempotents is normal, it is of interest to investigate the structure of these ordered orthodox semigroups via the Yamada decomposition. What is hard in such matters, and no exception here, is how to marry together the order theoretic structure with the algebraic structure theory. Basically, the problem is how to define orders on the building bricks of the structure theory in such a way that the algebraic isomorphisms become order isomorphisms. This we are able to do for a variety of different types, obtaining structure theorems which concern not only cartesian orders but also several new types of lexicographic orders. Examples are given to illustrate the hierarchy of orders and the corresponding algebraic conditions required for the order isomorphisms.

AB - The structure of orthodox semigroups with a normal band of idempotents has been described by Yamada. Since, for a naturally ordered strong Dubreil-Jacotin orthodox semigroup, it can be shown that the band of idempotents is normal, it is of interest to investigate the structure of these ordered orthodox semigroups via the Yamada decomposition. What is hard in such matters, and no exception here, is how to marry together the order theoretic structure with the algebraic structure theory. Basically, the problem is how to define orders on the building bricks of the structure theory in such a way that the algebraic isomorphisms become order isomorphisms. This we are able to do for a variety of different types, obtaining structure theorems which concern not only cartesian orders but also several new types of lexicographic orders. Examples are given to illustrate the hierarchy of orders and the corresponding algebraic conditions required for the order isomorphisms.

UR - http://www.scopus.com/inward/record.url?scp=0040676048&partnerID=8YFLogxK

U2 - 10.1080/00927879208824397

DO - 10.1080/00927879208824397

M3 - Article

AN - SCOPUS:0040676048

VL - 20

SP - 1167

EP - 1199

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 4

ER -