The Jordan-Zassenhaus theorem and direct decompositions
DOI10.1006/jabr.2000.8416zbMath0964.16017OpenAlexW2008194377MaRDI QIDQ1582252
Publication date: 2 May 2001
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jabr.2000.8416
ordersdirect summandslatticesgenusDedekind domainssemisimple algebrastorsion-free modulesdirect decompositionsalmost cancellation property
Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Structure, classification theorems for modules and ideals in commutative rings (13C05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)
Related Items (3)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Krull-Schmidt and cancellation over local rings
- Equivalent forms of Hensel's lemma
- Power cancellation of modules
- The genus of a module. II: Roiter's theorem, power cancellation and extension of scalars
- Cancellation of modules and groups and stable range of endomorphism rings
- Finite rank torsion free Abelian groups and rings
- Power-cancellation of groups and modules
- Summands of finite rank torsion free abelian groups
- On a special class of Dedekind domains
- Every Abelian group is a class group
- K-theory of finite groups and orders. Notes by E. Graham Evans
- Lattices over orders I
- On endomorphism rings of modules over henselian rings1
- Decomposition Problems for Modules Over Valuation Domains
- Multiply Maximally Complete Fields
- Endomorphism Rings and Direct Sums of Torsion Free Abelian Groups
- Pathological Modules over Tame Rings
- Krull-Schmidt Fails for Artinian Modules
- Modules with Semi-Local Endomorphism Ring
- On the decomposition of modules
- R-orders in a Split Algebra have Finitely Many Non-Isomorphic Irreducible Lattices as soon as R has Finite Class Number
- Every Countable Reduced Torsion-Free Ring is an Endomorphism Ring
- On semilocal rings
This page was built for publication: The Jordan-Zassenhaus theorem and direct decompositions