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Principal Elements of Lattices of Ideals

P. J. McCarthy
Proceedings of the American Mathematical Society
Vol. 30, No. 1 (Sep., 1971), pp. 43-45
DOI: 10.2307/2038216
Stable URL: http://www.jstor.org/stable/2038216
Page Count: 3
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Principal Elements of Lattices of Ideals
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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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