Semi-hereditary orders in a simple artinian ring

DOI10.1080/00927879408825129zbMath0812.16020OpenAlexW1971484270MaRDI QIDQ4310009

Hidetoshi Marubayashi, Haruo Miyamoto, Akira Ueda, Yi-cai Zhao

Publication date: 22 November 1994

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

Full work available at URL: https://doi.org/10.1080/00927879408825129

zbMATH Keywords

maximal ideallocalizationPrüfer domainmaximal right idealsidealizerHenselizationcentral \(D\)-orderfinite dimensional central simple \(F\)-algebralinearly ordered submodule latticesemi- hereditary \(D\)-orders

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Artinian rings and modules (associative rings and algebras) (16P20) Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. (16E60)

Related Items (2)

On semi-hereditary orders integral over a commutative valuation ring. ⋮ Weak crossed-product orders over valuation rings.

Cites Work

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• Right Noetherian rings integral over their centers
• Dubrovin valuation rings and Henselization
• Prime ideals in PI-rings
• Maximal orders over valuation rings
• Serial rings and finitely presented modules
• Maximal orders over Krull domains
• Non-commutative Dedekind rings
• Idealizers and hereditary Noetherian prime rings
• Semi-Prime Rings with Maximum Condition
• Torsion-Free and Divisible Modules Over Non-Integral-Domains
• Prime PI-rings in which finitely generated right ideals are principal
• Semihereditary prime algebras
• Groups Acting on Hereditary Rings
• Hereditary Commutative Rings and Centres of Hereditary Rings

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