TY - JOUR

T1 - Amenable orders associated with inverse transversals

AU - Blyth, Tom S.

AU - Santos, Maria Helena Coutinho Gomes de Almeida

PY - 2001/6/1

Y1 - 2001/6/1

N2 - If S is a regular semigroup with an inverse transversal S degrees = {x degrees ;x is an element of S} then an order less than or equal to on S is said to be amenable with respect to S degrees if (1) less than or equal to is compatible with the multiplication of S; (2) on the idempotents, less than or equal to coincides with the natural order less than or equal to (n): (3) x less than or equal to y double right arrow x degreesx less than or equal to (n) y degreesy, xx degrees less than or equal to (n) yy degrees. This notion is in fact independent of the choice of inverse transversal. Here we consider the case where S is locally inverse (equivalently, where S-degrees is a quasi-ideal). We give a complete description of all amenable orders on S and characterise the natural order less than or equal to (n) as the smallest of these. We also establish a bijection from the set of amenable orders definable on S to the set of McAlister cones of S degrees, whence every amenable order on S degrees extends to a unique amenable order on S. (C) 2001 Academic Press

AB - If S is a regular semigroup with an inverse transversal S degrees = {x degrees ;x is an element of S} then an order less than or equal to on S is said to be amenable with respect to S degrees if (1) less than or equal to is compatible with the multiplication of S; (2) on the idempotents, less than or equal to coincides with the natural order less than or equal to (n): (3) x less than or equal to y double right arrow x degreesx less than or equal to (n) y degreesy, xx degrees less than or equal to (n) yy degrees. This notion is in fact independent of the choice of inverse transversal. Here we consider the case where S is locally inverse (equivalently, where S-degrees is a quasi-ideal). We give a complete description of all amenable orders on S and characterise the natural order less than or equal to (n) as the smallest of these. We also establish a bijection from the set of amenable orders definable on S to the set of McAlister cones of S degrees, whence every amenable order on S degrees extends to a unique amenable order on S. (C) 2001 Academic Press

UR - http://www.scopus.com/record/display.uri?eid=2-s2.0-0035374146&origin=resultslist&sort=plf-f&src=s&st1

U2 - 10.1006/jabr.2001.8730

DO - 10.1006/jabr.2001.8730

M3 - Article

VL - 240

SP - 143

EP - 164

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -