Lattices of annihilators in commutative algebras over fields.

DOI10.1515/dema-2015-0039zbMath1343.06004OpenAlexW2498276374MaRDI QIDQ895875

Małgorzata Jastrzębska, Jan Krempa

Publication date: 7 December 2015

Published in: Demonstratio Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/dema-2015-0039

zbMATH Keywords

finite dimensional algebrasposetslocal algebraslattices of annihilators

Mathematics Subject Classification ID

Representation theory of lattices (06B15) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

Cites Work

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• Very long chains of annihilator ideals
• Rings in which annihilators form a sublattice of the lattice of ideals
• Every finite lattice can be embedded in a finite partition lattice
• Congruence lattices of finite algebras and intervals in subgroup lattices of finite groups
• Representation of finite lattices by annihilators of completely 0-simple semigroups
• The subalgebra lattice of a finite algebra
• On quasi-Frobenius semigroup algebras

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