Modules of projective dimension one over noncommutative prüfer rings

DOI10.1080/00927879408825024zbMath0808.16010OpenAlexW1972256306MaRDI QIDQ4300609

Yiqiang Zhou

Publication date: 16 August 1994

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

Full work available at URL: https://doi.org/10.1080/00927879408825024

zbMATH Keywords

direct sumsdirect summandsfinitely presentednoncommutative Prüfer ringsprime Goldie ringfinitely generated right idealprojective generatordivisible \(R\)-modulesprojective dimension at most 1well- ordered continuous chain

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Divisibility, noncommutative UFDs (16U30) Homological dimension in associative algebras (16E10) Ore rings, multiplicative sets, Ore localization (16U20) Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) (16P70)

Related Items

Relative n-rigid objects in (n + 2)-angulated categories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Divisible modules over integral domains
• Noncommutative Prüfer rings
• Injective Modules Over Prufer Rings
• Noncommutative prufer rings and some generalizations
• Coherent Rings and Fp -Injective Modules
• Absolutely Pure Modules