Torsion in class groups of modules over certain one-dimensional rings

DOI10.1080/00927879908826693zbMath0959.16001OpenAlexW2041707552MaRDI QIDQ4262370

Christopher J. Pappacena

Publication date: 4 June 2000

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

Full work available at URL: https://doi.org/10.1080/00927879908826693

zbMATH Keywords

ordersKrull dimension oneaffine semiprime Noetherian PI algebrasgenus class groupstorsion in class groups

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Class groups and Picard groups of orders (11R65) Semiprime p.i. rings, rings embeddable in matrices over commutative rings (16R20)

Cites Work

• The genus of a module
• The genus of a module. II: Roiter's theorem, power cancellation and extension of scalars
• Integral ring homomorphisms
• Cancellation and direct summands in dimension 1
• Algebras over zero-dimensional rings
• Multiplicative groups of fields modulo products of subfields
• On the Picard group: Torsion and the kernel induced by a faithfully flat map
• Galois Groups and the Multiplicative Structure of Field Extensions
• On Invertible Bimodules and Automorphisms of Noncommutative Rings
• On the decomposition of modules
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