On principal element lattices

DOI10.1007/S00012-021-00714-9zbMath1471.13009OpenAlexW3135492455MaRDI QIDQ2663184

Gülşen Ulucak, Suat Koç, Unsal Tekir, Kar Ping Shum

Publication date: 16 April 2021

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00012-021-00714-9

zbMATH Keywords

principal element latticePrüfer latticeprincipal element\(l\)-prime element\(S\)-lattice

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Ordered semigroups and monoids (06F05) Noether lattices (06F10)

Cites Work

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• Abstract commutative ideal theory
• Abstract commutative ideal theory without chain condition
• Dilworth's principal elements
• \(\ell \)-prime elements in multiplicative lattices.
• Almost principal element lattices
• Noetherian lattices in which every element is a product of primary elements
• \(s\)-prime elements in multiplicative lattices
• Some results on almost principal element lattices
• Structure of Noether lattices with join-principal maximal elements
• Principal element lattices
• Laskerian Lattices
• Primary elements in Prüfer lattices
• Almost π-Lattices
• 2-join decomposition lattices.

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