$\mathfrak{X}$-elements in multiplicative lattices -- A generalization of $J$-ideals, $n$-ideals and $r$-ideals in rings

zbMath1492.13005arXiv2101.06667MaRDI QIDQ5092491

Vinayak Joshi, Sachin Sarode

Publication date: 22 July 2022

Full work available at URL: https://arxiv.org/abs/2101.06667

zbMATH Keywords

commutative ringprime elementmultiplicative lattice\(n\)-ideal\(J\)-ideal\(r\)-ideal\(\mathfrak{X}\)-element\(J\)-element\(n\)-element\(r\)-element

Mathematics Subject Classification ID

Structure, classification theorems for modules and ideals in commutative rings (13C05) Ideals and multiplicative ideal theory in commutative rings (13A15) Algebraic aspects of posets (06A11) Noether lattices (06F10)

Cites Work

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• Abstract commutative ideal theory
• Fractional elements in multiplicative lattices
• Abstract commutative ideal theory without chain condition
• Some results on abstract commutative ideal theory
• \(s\)-prime elements in multiplicative lattices
• On lattice-ordered commutative semigroups
• Strong compact elements in multiplicative lattices
• Primary elements in Prüfer lattices
• N-ideals of commutative rings
• 2-Absorbing and Weakly 2-Absorbing Elements in Multiplicative Lattices
• $r$-ideals in commutative rings
• Residuated Lattices

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