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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
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0279080-4
PII: S 0002-9939(1971)0279080-4
Keywords: Principal element, invertible ideal
Article copyright: © Copyright 1971 American Mathematical Society