ORE EXTENSIONS OF WEAK ZIP RINGS

DOI10.1017/S0017089509005151zbMath1186.16017OpenAlexW2147713538MaRDI QIDQ3183178

Lunqun Ouyang

Publication date: 19 October 2009

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0017089509005151

zbMATH Keywords

nilpotent elementsOre extensionssemicommutative ringsreduced ringsupper triangular matrix ringsreversible ringsleft weak zip ringsright weak annihilators

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Ordinary and skew polynomial rings and semigroup rings (16S36) Automorphisms and endomorphisms (16W20) Generalizations of commutativity (associative rings and algebras) (16U80) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

Related Items

On rings with weak property (A) and their extensions ⋮ On Rings Having McCoy-Like Conditions ⋮ Nilpotent elements of skew Hurwitz series rings ⋮ On Weak Annihilator Ideals of Skew Monoid Rings ⋮ On zip and weak zip rings of skew generalized power series. ⋮ \(\pi\)-Armendariz rings relative to a monoid ⋮ McCoy property and nilpotent elements of skew generalized power series rings ⋮ Study of skew inverse Laurent series rings ⋮ Nil-Armendariz condition on skew generalized power series rings ⋮ Mal'cev-Neumann series over rings satisfy the weak Beachy-Blair condition ⋮ ON WEAK ZIP SKEW POLYNOMIAL RINGS ⋮ Skew Poincaré-Birkhoff-Witt extensions over weak zip rings ⋮ Annihilator Properties of Skew Monoid Rings ⋮ MAL'CEV–NEUMANN SERIES OVER ZIP AND WEAK ZIP RINGS ⋮ A GENERALIZATION OF NIL-ARMENDARIZ RINGS ⋮ Unnamed Item ⋮ Algebraic frames in which dense elements are above dense compact elements

Cites Work

• Rings with zero intersection property on annihilators: zip rings
• Rings whose faithful left ideals are cofaithful
• Armendariz rings
• Ore extensions of Baer and p.p.-rings.
• Extensions of zip rings.
• Semi-commutativity and the McCoy condition.
• Annihilator ideals, associated primes and kasch-mccoy commutative rings
• The Finite Intersection Property on Annihilator Right Ideals
• Primeness, semiprimeness and prime radical of ore extensions
• ARMENDARIZ RINGS AND SEMICOMMUTATIVE RINGS
• On Weak Armendariz Rings
• On annihilator ideals of a polynomial ring over a noncommutative ring

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