Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Ordered inverse semigroups


Author: Tôru Saitô
Journal: Trans. Amer. Math. Soc. 153 (1971), 99-138
MSC: Primary 06.70
MathSciNet review: 0270990
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we consider two questions: one is to characterize the structure of ordered inverse semigroups and the other is to give a condition in order that an inverse semigroup is orderable.

The solution of the first question is carried out in terms of three types of mappings. Two of these consist of mappings of an $ \mathcal{R}$-class onto an $ \mathcal{R}$-class, while one of these consists of mappings of a principal ideal of the semilattice $ E$ constituted by idempotents onto a principal ideal of $ E$.

As for the second question, we give a theorem which extends a well-known result about groups that a group $ G$ with the identity $ e$ is orderable if and only if there exists a subsemigroup $ P$ of $ G$ such that $ P \cup {P^{ - 1}} = G,P \cap {P^{ - 1}} = \{ e\} $ and $ xP{x^{ - 1}} \subseteqq P$ for every $ x \in G$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 06.70

Retrieve articles in all journals with MSC: 06.70


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0270990-5
PII: S 0002-9947(1971)0270990-5
Keywords: Inverse semigroup, left ordered inverse semigroup, ordered inverse semigroup, tree semilattice, left orderability of inverse semigroups, orderability of inverse semigroups
Article copyright: © Copyright 1971 American Mathematical Society