Some results on abstract commutative ideal theory

DOI10.1007/BF01876923zbMath0822.06015OpenAlexW2056045330MaRDI QIDQ1346386

Francisco Alarcón, C. Jayaram, Daniel D. Anderson

Publication date: 28 September 1995

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01876923

zbMATH Keywords

Boolean algebrafiltersNakayama lemmaregular latticesKrull intersection theoremmultiplicative lattice

Mathematics Subject Classification ID

Boolean algebras (Boolean rings) (06E99) Ordered structures (06F99)

Related Items (26)

Weakly Prime Elements in Multiplicative Lattices ⋮ Diameter and girth of the multiplicative zero-divisor graph of multiplicative lattices ⋮ Zariski topology on lattice modules ⋮ Almost π-Lattices ⋮ On \(\phi\)-absorbing primary elements in lattice modules ⋮ Some remarks on Dedekind lattices ⋮ \(s\)-prime elements in multiplicative lattices ⋮ Some results on almost principal element lattices ⋮ Comaximal factorization lattices ⋮ Principal element lattices ⋮ An element weakly primary to another element. ⋮ On the Zariski topology over an $L$-module $M$ ⋮ Quasiregular and Baer lattices. II ⋮ 2-Absorbing and Weakly 2-Absorbing Elements in Multiplicative Lattices ⋮ Weak complemented and weak invertible elements in \(C\)-lattices ⋮ $\mathfrak{X}$-elements in multiplicative lattices -- A generalization of $J$-ideals, $n$-ideals and $r$-ideals in rings ⋮ Laskerian Lattices ⋮ On the second radical elements of lattice modules ⋮ Second classical Zariski topology on second spectrum of lattice modules ⋮ On minimal spectrum of multiplication lattice modules ⋮ Zariski second radical elements of lattice modules ⋮ Unnamed Item ⋮ Strong compact elements in multiplicative lattices ⋮ Unnamed Item ⋮ Ideal divisibility monoids ⋮ σ-Elements in Multiplicative Lattices

Cites Work

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• Join-principally generated multiplicative lattices
• Abstract commutative ideal theory
• Union conditions in r-lattices
• Abstract commutative ideal theory without chain condition
• Principal multiplicative lattices
• Rings in which semi-primary ideals are primary
• Multiplication Rings as Rings in Which Ideals with Prime Radical are Primary
• Idempotent Noether Lattices
• Union Conditions in Noether Lattices
• Equivalent Conditions for a Ring to Be a Multiplication Ring
• On Complete Lattices and a Problem of Birkhoff and Frink

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