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A two-dimensional domain whose integral closure is not t-linked.

Dumitrescu, Tiberiu — 2001

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

A class of multiplicative lattices

Tiberiu Dumitrescu; Mihai Epure — 2021

Czechoslovak Mathematical Journal

We study the multiplicative lattices $L$ which satisfy the condition $a = (a : (a : b)) (a : b)$ for all $a, b \in L$ . 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 $ℤ$ or $ℝ$ . 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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