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A class of multiplicative lattices

Tiberiu DumitrescuMihai Epure — 2021

Czechoslovak Mathematical Journal

We study the multiplicative lattices L which satisfy the condition a = ( a : ( a : b ) ) ( a : b ) for all a , b L . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group or . A sharp lattice L localized at its maximal elements are totally ordered sharp lattices. The converse is true if L has finite character.

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