On the krull-schmidt-azumaya theorem for integral group rings

DOI10.1080/00927879808826371zbMath0914.20003OpenAlexW1974316670MaRDI QIDQ4216829

Lee Klingler, Charles J. Odenthal, Peter Hindman

Publication date: 17 June 1999

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

Full work available at URL: https://doi.org/10.1080/00927879808826371

zbMATH Keywords

finite groupsAbelian \(p\)-groupslatticesdihedral 2-groupsmaximal ordersintegral group ringsdirect sum decompositionsKrull-Schmidt-Azumaya theoremtorsion free cancellation

Mathematics Subject Classification ID

Group rings (16S34) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Integral representations of finite groups (20C10) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

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Cites Work

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• Failure of the Krull-Schmidt theorem for integral representations
• Cancellation over commutative rings of dimension one and two
• Cancellation and direct summands in dimension 1
• Presentations over HNP rings with enough invertible ideals and torsionfree cancellation over neoclassical orders
• Mixed modules over ZG, G cyclic of prime order, and over related Dedekind pullbacks
• The class groups of quaternion and dihedral 2‐groups
• Krull-Schmidt theorems in dimension 1

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