Vol. 33, No. 3, 1970

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Principal multiplicative lattices

Melvin F. Janowitz

Vol. 33 (1970), No. 3, 653–656
Abstract

P. J. McCarthy has recently proved that if R is a Noetherian ring with unity, then every ideal of R is a principal element of L(R), the lattice of ideals of R, if and only if R is a multiplication ring. It is shown here that an arbitrary commutative ring R with unity is a Noetherian multiplication ring if and only if every ideal of R is a principal element of L(R).

Mathematical Subject Classification
Primary: 13.25
Milestones
Received: 18 August 1969
Published: 1 June 1970
Authors
Melvin F. Janowitz