Abstract commutative ideal theory
From MaRDI portal
Publication:1131274
DOI10.2140/pjm.1962.12.481zbMath0111.04104OpenAlexW4254225449MaRDI QIDQ1131274
Publication date: 1962
Published in: Pacific Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2140/pjm.1962.12.481
Lattice ideals, congruence relations (06B10) Ideals and multiplicative ideal theory in commutative rings (13A15)
Related Items
Tertiary decompositions in lattice modules ⋮ Associated and weakly associated prime elements and primary decomposition in lattice modules ⋮ Primary elements in Prüfer lattices ⋮ Some results on abstract commutative ideal theory ⋮ Tidy Noether lattices ⋮ Characterization of a class of \(r\)-lattices ⋮ Prime, weakly prime and almost prime elements in multiplication lattice modules ⋮ Regular ideals in commutative rings, sublattices of regular ideals, and Prüfer rings ⋮ Almost π-Lattices ⋮ On \(\phi\)-absorbing primary elements in lattice modules ⋮ Modules: Duals and principally generated fake duals ⋮ Noetherian lattices in which every element is a product of primary elements ⋮ Unnamed Item ⋮ Some remarks on Dedekind lattices ⋮ Rees valuations and asymptotic primes of rational powers in noetherian rings and lattices ⋮ \(s\)-prime elements in multiplicative lattices ⋮ Some results on almost principal element lattices ⋮ Self-duality and co-multiplication lattices ⋮ Obituary: R. P. Dilworth ⋮ Comaximal factorization lattices ⋮ Principal element lattices ⋮ On principal element lattices ⋮ Relationship between Noether lattices andx-systems ⋮ Unnamed Item ⋮ Artinian ring and amalgamated algebra along an ideal ⋮ Quasi-complete Semilocal Rings and Modules ⋮ Radical factorization in commutative rings, monoids and multiplicative lattices ⋮ Integral closure in multiplicative lattices ⋮ Lattices of order ideals on ordered semigroups ⋮ Open set lattices of subspaces of spectrum spaces ⋮ Regularity in Terms of Reductions in Local Noether Lattices ⋮ Invertibility, Semistar Operations, and the Ring of Finite Fractions ⋮ Completeness in semi-local ideal lattices ⋮ Nonimbeddable Noether Lattices ⋮ Structure and embedding theorems for small strong-pi-lattices ⋮ Idempotent Noether Lattices ⋮ Noetherian properties in monoid rings. ⋮ A note on regular local Noether lattices ⋮ Unnamed Item ⋮ Completions of Macaulay local lattices ⋮ An element weakly primary to another element. ⋮ Principal Elements of Lattices of Ideals ⋮ On the Zariski topology over an $L$-module $M$ ⋮ On prime divisors of large powers of elements in Noether lattices ⋮ Quasiregular and Baer lattices. II ⋮ Union Conditions in Noether Lattices ⋮ Semiprime elements and relative annihilators in multiplicative lattices ⋮ 2-Absorbing and Weakly 2-Absorbing Elements in Multiplicative Lattices ⋮ A note on Noether lattices in which each element is primary ⋮ Weak complemented and weak invertible elements in \(C\)-lattices ⋮ On Nagata rings with amalgamation properties ⋮ $\mathfrak{X}$-elements in multiplicative lattices -- A generalization of $J$-ideals, $n$-ideals and $r$-ideals in rings ⋮ Principal mappings between posets ⋮ A note on regular local Noether lattices II ⋮ Join-Principal Elements in Noether Lattices ⋮ Maximal elements and completions of Noether lattices ⋮ Abstract commutative ideal theory without chain condition ⋮ Laskerian Lattices ⋮ Fake rings, fake modules, and duality ⋮ Approximately Gorenstein lattices ⋮ Commutative ideal theory without finiteness conditions: Completely irreducible ideals ⋮ Unique factorization and small regular local Noether lattices ⋮ Principal Ideals in the Ideal Lattice ⋮ On theory of x-ideals ⋮ Dilworth's principal elements ⋮ On minimal spectrum of multiplication lattice modules ⋮ Arithmetical rings and multiplicative lattices ⋮ Unnamed Item ⋮ Divisibility theory in commutative rings: Bezout monoids ⋮ Strong compact elements in multiplicative lattices ⋮ Ideal theory in commutative semigroups ⋮ Join-principally generated multiplicative lattices ⋮ Ideal divisibility monoids ⋮ On the prime spectrum of an le-module
