Bezout rings and serial rings

DOI10.1080/00927877908822361zbMath0397.16007OpenAlexW2124295117MaRDI QIDQ4180477

Robert B. jun. Warfield

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1080/00927877908822361

zbMATH Keywords

Jacobson RadicalPrime RadicalRight Bezout RingArtinian Principal Ideal RingArtinian Quotient RingsBezout OrderOre DomainRight Goldie Bezout Ring

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Generalizations of commutativity (associative rings and algebras) (16U80) Divisibility, noncommutative UFDs (16U30) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Localization and associative Noetherian rings (16P50)

Related Items

Rings with finite reduced rank, Leavitt path algebras are Bézout, Localization and ideal theory in Noetherian strongly group-graded rings, Artinian quotient rings of power-series rings, Serial rings with krull dimension, P.I. rings and the localization at height 1 prime ideals, On dominance, On semilocal, Bézout and distributive generalized power series rings, Classical Quotient Rings of Group Graded Rings, Classical localizations in serial rings, Endomorphism rings, power series rings, and serial modules, Modules over serial rings, Unnamed Item, Unnamed Item, Quotient rings, chain conditions and injective ring endomorphisms, The ring of Colombeau’s full generalized quaternions, Semidistributive modules, On reduced rank of triangular matrix rings, Rings of the Morita Contexts and Semihereditary MaximalV-Orders, Modules, On noncommutative piecewise Noetherian rings

Cites Work

• Non-commutative principal ideal rings
• Cancellation of modules and groups and stable range of endomorphism rings
• Serial rings and finitely presented modules
• Decomposition of Noetherian Rings
• Rings in Which Finitely Generated Right Ideals are Principal^†