Displaying similar documents to “Representation of algebraic distributive lattices with ℵ1 compact elements as ideal lattices of regular rings.”

Generators of existence varieties of regular rings and complemented Arguesian lattices

Christian Herrmann, Marina Semenova (2010)

Open Mathematics

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We proved in an earlier work that any existence variety of regular algebras is generated by its simple unital Artinian members, while any existence variety of Arguesian sectionally complemented lattices is generated by its simple members of finite length. A characterization of the class of simple unital Artinian members [members of finite length, respectively] of such varieties is given in the present paper.

A note on Stone join-semilattices

Shriram Nimbhorkar, Anwari Rahemani (2011)

Open Mathematics

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Characterizations for a pseudocomplemented modular join-semilattice with 0 and 1 and its ideal lattice to be a Stone lattice are given.

Finite atomistic lattices that can be represented as lattices of quasivarieties

K. Adaricheva, Wiesław Dziobiak, V. Gorbunov (1993)

Fundamenta Mathematicae

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We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].