In:
Glasgow Mathematical Journal, Cambridge University Press (CUP), Vol. 9, No. 1 ( 1968-01), p. 12-21
Abstract:
Various semigroups of partial transformations (and more generally, semigroups of binary relations) on a set have been studied by a number of Soviet mathematicians; to mention only a few: Gluskin [2], Ljapin [4] , Shutov [6], Zaretski [7] , [8]. In their study the densely embedded ideal of a semigroup introduced by Ljapin [4] plays a central role. In fact, a concrete semigrou Q is described in several instances by its abstract characteristic, namely either by a set of postulates on an abstract semigroup or by a set of postulates (which are usually much simpler) on an abstract semigroup S which is a densely embedded ideal of a semigroup T isomorphic to Q . In many cases, the densely embedded ideal S is a completely 0-simple semigroup. The following theorem [3, 1.7.1] reduces the study of a semigroup Q with a weakly reductive densely embedded ideal S to the study of the translational hull of S : Theorem (Gluskin). If S is a weakly reductive densely embedded ideal of a semigroup Q, then Q is isomorphic to the translational hull ω( S ) of S .
Type of Medium:
Online Resource
ISSN:
0017-0895
,
1469-509X
DOI:
10.1017/S0017089500000240
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1968
detail.hit.zdb_id:
1465410-6
SSG:
17,1
Bookmarklink