On semi-hereditary orders integral over a commutative valuation ring.

DOI10.1016/j.jalgebra.2001.10.001zbMath1058.16019OpenAlexW1997962870MaRDI QIDQ1886817

Hidetoshi Marubayashi

Publication date: 19 November 2004

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2001.10.001

zbMATH Keywords

idempotent maximal idealssemi-hereditary orderssimple Artinian ringscommutative valuation ringsfinitely generated left ideals

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Ideals in associative algebras (16D25) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. (16E60)

Cites Work

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• Ideals of hereditary Noetherian prime rings
• Maximal orders over valuation rings
• Integral semihereditary orders, extremality, and Henselization
• Integral semihereditary orders inside a Bézout maximal order
• Non-commutative valuation rings and semi-hereditary orders
• Skew group rings which are semi-hereditary orders and Prüfer orders in simple Artinian rings
• Hereditary Noetherian prime rings
• Valuation theory
• Infinite Crossed Products and Group-Graded Rings
• On Semihereditary Maximal Orders
• Semi-hereditary orders in a simple artinian ring
• Dubrovin valuation properties of skew group rings and crossed products
• Bounded Hereditary Noetherian Prime Rings

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