Right P-Comparable Semigroups

Halimi, Nazer H. (2013) Right P-Comparable Semigroups. Communications in Algebra, 41 4: 1442-1457. doi:10.1080/00927872.2011.643838


Author Halimi, Nazer H.
Title Right P-Comparable Semigroups
Journal name Communications in Algebra   Check publisher's open access policy
ISSN 0092-7872
1532-4125
Publication date 2013-04-01
Year available 2013
Sub-type Article (original research)
DOI 10.1080/00927872.2011.643838
Volume 41
Issue 4
Start page 1442
End page 1457
Total pages 16
Place of publication Philadelphia, United States
Publisher Taylor & Francis
Language eng
Formatted abstract
In this article we utilise the notion of right waist and right comparizer to study the ideal theory of semigroups. We also consider which of the properties of right cones can be carried over to right P-comparable semigroups. We give sufficient and necessary conditions on the set of nilpotent elements of a semigroup to be an ideal, and we provide several equivalent characterizations for a right ideal being a right waist. In one of our main results we show that in a right P1-comparable semigroup with left cancellation law, a prime segment P2P1 is Archimedean, simple or exceptional. This extends a similar result pertaining to right cones.
Keyword P-comparable semigroups
Prime segments
Right comparizer ideals
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
 
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