Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Principal elements of lattices of ideals

Author: P. J. McCarthy
Journal: Proc. Amer. Math. Soc. 30 (1971), 43-45
MSC: Primary 13.10
MathSciNet review: 0279080
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The notion of principal element of a commutative multiplicative lattice was introduced by Dilworth. In this note the principal elements of the lattice of ideals of a commutative ring with unity R are characterized as those ideals of R which are finitely generated and locally principal ideals. It follows that a regular ideal of R is a principal element of the lattice of ideals of R if and only if it is invertible.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13.10

Retrieve articles in all journals with MSC: 13.10

Additional Information

PII: S 0002-9939(1971)0279080-4
Keywords: Principal element, invertible ideal
Article copyright: © Copyright 1971 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia