INVERTIBLE IDEALS AND NON-COMMUTATIVE ARITHMETICS

DOI10.1081/AGB-100107952zbMath1001.16008OpenAlexW2042960465MaRDI QIDQ2777960

Wolfgang Rump

Publication date: 16 December 2002

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

Full work available at URL: https://doi.org/10.1081/agb-100107952

zbMATH Keywords

regular elementsmaximal idealsdecomposition theoremsquotient ringsNoetherian ringsinvertible idealsascending chain conditionlocalisationsAsano ordersfull idealsAsano ringsfull prime idealsmultiplicative semigroups of subbimodules

Mathematics Subject Classification ID

Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Ideals in associative algebras (16D25) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Noetherian rings and modules (associative rings and algebras) (16P40) Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) (16P70)

Related Items

Hereditary arithmetics ⋮ Global theory of lattice-finite Noetherian rings. ⋮ Factorizations in Bounded Hereditary Noetherian Prime Rings ⋮ Lattice-finite rings.