Nilpotent ideals in polynomial and power series rings

DOI10.1090/S0002-9939-10-10252-4zbMath1209.16014OpenAlexW1981141816MaRDI QIDQ3558990

Yang Lee, Chan Yong Hong, Pace P. Nielsen, Nam Kyun Kim, Victor P. Camillo

Publication date: 11 May 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-10-10252-4

zbMATH Keywords

nil idealspolynomial ringsnilpotent idealspower series ringsbounded index of nilpotencelocally nilpotent idealsleft \(T\)-nilpotent ideals

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Generalizations of commutativity (associative rings and algebras) (16U80)

Related Items (17)

Symmetry on zero and idempotents ⋮ Annihilating properties of ideals generated by coefficients of polynomials and power series ⋮ An alternative perspective on skew generalized power series rings ⋮ Reflexive property on nil ideals ⋮ On \(\sigma\)-nil ideals of bounded index of \(\sigma\)-nilpotence. ⋮ Unnamed Item ⋮ Radicals in skew polynomial and skew Laurent polynomial rings. ⋮ Structure of NI rings related to centers ⋮ NIL-ARMENDARIZ RINGS AND UPPER NILRADICALS ⋮ On Monoid Rings Over Nil Armendariz Ring ⋮ Radicals of skew polynomial rings and skew Laurent polynomial rings. ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Rings which satisfy the Property of Inserting Regular Elements at Zero Products ⋮ Insertion of units at zero products ⋮ RINGS OVER WHICH POLYNOMIAL RINGS ARE ARMENDARIZ AND REVERSIBLE ⋮ On a ring property related to nilradicals

Cites Work

• Goldie conditions for Ore extensions over semiprime rings.
• The nil radical of power series rings
• The sum of nil one-sided ideals of bounded index of a ring
• Radical endomorphisms of decomposable modules.
• Some aspects of T-nilpotence
• Rings of bounded index
• Amitsur's Conjecture on Polynomial Rings in <i>n</i> Commuting Indeterminates
• The Radical of the Row-Finite Matrices Over an Arbitrary Ring
• Zero Divisors and Nilpotent Elements in Power Series Rings
• A polynomial ring that is Jacobson radical and not nil.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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