Non commutative unique factorization rings

DOI10.1080/00927879108824136zbMath0722.16017OpenAlexW2026698397MaRDI QIDQ3209274

Shigeru Kobayashi, Hidetoshi Marubayashi, Akira Ueda, G. Q. Abbasi

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1080/00927879108824136

zbMATH Keywords

automorphismderivationskew polynomial ringgroup ringpolycyclic-by-finite groupnoncommutative unique factorization ringreflexive prime idealsUFR

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Group rings (16S34) Divisibility, noncommutative UFDs (16U30)

Related Items

Ore-Rees rings which are maximal orders., Generalized hereditary Noetherian prime rings, Examples of Ore extensions which are maximal orders whose based rings are not maximal orders, Positively graded rings which are maximal orders and generalized Dedekind prime rings, Positively graded rings which are unique factorization rings, The semicentre of a group algebra, Strongly graded rings which are generalized Dedekind rings, Multiplicative Ideal Theory in Noncommutative Rings, Factorizations of Elements in Noncommutative Rings: A Survey, SKEW POLYNOMIAL RINGS WHICH ARE GENERALIZED ASANO PRIME RINGS, Height-one prime ideals in semigroup algebras satisfying a polynomial identity

Cites Work

• Unnamed Item
• Unnamed Item
• Remarks on VHC-orders in a simple Artinian ring
• On v-ideals in a VHC order
• Generalized Rees rings and relative maximal orders satisfying polynomial identities
• Simple modules over hereditary Noetherian prime rings
• Anneaux de Krull non commutatifs
• Lectures on unique factorization domains. Notes by M. Pavman Murthy
• A krull type generalization of knp rings with enough Invertible ideals
• A skew polynomial ring over a v-hc order with enough V-inveriible ideals
• Idealizers in generalized krull orders
• Height One Primes of Polycyclic Group Rings
• Non-Commutative Unique Factorisation Rings
• Arithmetically graded rings revisited
• Three examples concerning the ore condition in Noetherian rings
• Irreducible Modules for Polycyclic Group Algebras
• Group rings which are v-HC orders and Krull orders
• Prime Ideals in Group Rings of Polycyclic Groups
• Divtsorially graded rings by polycyclic-by-finite groups
• A characterization of a non-frime v-hc order