Annihilator ideals, associated primes and kasch-mccoy commutative rings

DOI10.1080/00927879108824235zbMath0729.16015OpenAlexW2027054187MaRDI QIDQ3353200

Carl Faith

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1080/00927879108824235

zbMATH Keywords

associated primesright annihilatorfaithful idealright zip ringannihilator right idealsKasch classical quotient ringright E-max

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Polynomials over commutative rings (13B25) Ideals in associative algebras (16D25) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Local rings and semilocal rings (13H99) Rings of fractions and localization for commutative rings (13B30) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (43)

On Ore extension and skew power series rings with some restrictions on zero-divisors ⋮ On seminoetherian rings and modules ⋮ On Rings Having McCoy-Like Conditions ⋮ Unnamed Item ⋮ Nilpotent elements of skew Hurwitz series rings ⋮ On zip and weak zip rings of skew generalized power series. ⋮ Countably McCoy rings ⋮ On Property (A) of rings and modules over an ideal ⋮ ORE EXTENSIONS OF WEAK ZIP RINGS ⋮ Generalized Malcev-Neumann series modules with the Beachy-Blair condition. ⋮ On transfer of annihilator conditions of rings ⋮ ON GENERALIZED ZIP RINGS ⋮ McCoy property and nilpotent elements of skew generalized power series rings ⋮ On weak annihilators and nilpotent associated primes of skew PBW extensions ⋮ On a theorem of McCoy ⋮ Nil-Armendariz condition on skew generalized power series rings ⋮ Zip rings (resp. czip rings) and some applications ⋮ Polynomial rings over Goldie-Kerr commutative rings II ⋮ Unnamed Item ⋮ When is the idealization R⋉M an 𝒜-ring? ⋮ On proper strong Property (𝒜) for rings and modules ⋮ Trace properties in rings with zero divisors ⋮ Skew polynomial extensions over zip rings. ⋮ Unnamed Item ⋮ ON WEAK ZIP SKEW POLYNOMIAL RINGS ⋮ Skew Poincaré-Birkhoff-Witt extensions over weak zip rings ⋮ Annihilator Properties of Skew Monoid Rings ⋮ The Mori property in rings with zero divisors. II. ⋮ Polynomial Rings Over Goldie-Kerr Commutative Rings ⋮ A GENERALIZATION OF NIL-ARMENDARIZ RINGS ⋮ Unnamed Item ⋮ The diameter of a zero divisor graph ⋮ The McCoy condition on skew Poincaré-Birkhoff-Witt extensions ⋮ Zip rings and mal'cev domains ⋮ On the vanishing of annihilators of modules ⋮ On commutative trivial extensions ⋮ Annihilator conditions on modules over commutative rings ⋮ On property (𝒜) for modules over direct products of rings ⋮ Solution of an open problem on cofaithful one-sided ideals ⋮ On property () of the amalgamated duplication of a ring along an ideal ⋮ Associated primes in commutative polynomial rings ⋮ Characterizations of rings by their modules ⋮ Algebraic frames in which dense elements are above dense compact elements

Cites Work

• Rings with zero intersection property on annihilators: zip rings
• The descending chain condition relative to a torsion theory
• Dual generalizations of the Artinian and Noetherian conditions
• Maximal quotient rings of ring extensions
• Quotient rings and direct products of full linear rings
• \(\Sigma\)-injective modules
• Grundlagen einer Theorie der Frobeniuserweiterungen
• Zip rings and mal'cev domains
• Commutative rings whose quotients are Goldie
• Commutative Quasi-Frobenius Rings
• Rings with Ascending Condition on Annihilators
• The Dual of the Notion of “Finitely Generated”
• On Quasi‐Artinian Rings

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