Principal elements of lattices of ideals

McCarthy, P. J.

doi:10.1090/S0002-9939-1971-0279080-4

Principal elements of lattices of ideals
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by P. J. McCarthy PDF

Proc. Amer. Math. Soc. 30 (1971), 43-45 Request permission

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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