Algebra Commons^™

Lattice-Ordered Algebras That Are Subdirect Products Of Valuation Domains, Melvin Henriksen, Suzanne Larson, Jorge Martinez, R. G. Woods

Suzanne Larson

An f-ring (i.e., a lattice-ordered ring that is a subdirect product of totally ordered rings) A is called an SV-ring if A/P is a valuation domain for every prime ideal P of A. If M is a maximal ℓ-ideal of A , then the rank of A at M is the number of minimal prime ideals of A contained in M, rank of A is the sup of the ranks of A at each of its maximal ℓ-ideals. If the latter is a positive integer, then A is said to have finite rank, and if A = C(X) is the …