A survey of integral representation theory

DOI10.1090/S0002-9904-1970-12441-7zbMath0194.04701MaRDI QIDQ5589399

Irving Reiner

Publication date: 1970

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

group theory

Related Items (19)

The Grothendieck and Picard groups of finite rank torsion free \(\mathfrak{sl}(2)\)-modules ⋮ Almost Split Sequences in Dimension One ⋮ Matrix zeros of quadratic equations ⋮ An integral theory of dominant dimension of Noetherian algebras ⋮ Integral bases and invariant vectors for Weil representations ⋮ Unnamed Item ⋮ Class groups of integral group rings ⋮ Sur la structure galoisienne du groupe des unites d'un corps abelien réel de type (p,p) ⋮ A homotopy classification of 2-complexes with finite cyclic fundamental group ⋮ The Picard group of noncommutative rings, in particular of orders ⋮ Computing the ideal class monoid of an order ⋮ Class Groups of Integral Group Rings ⋮ FACTOR EQUIVALENCE OF GALOIS MODULES AND REGULATOR CONSTANTS ⋮ Nilpotent elements in integral representation rings of Hopf-algebra orders in group algebras of prime order ⋮ Sur la structure galoisienne du groupe des unités d'un corps abélien de type \((p,p)\) ⋮ Regulator constants of integral representations of finite groups ⋮ Matrices and pairs of modules ⋮ A Mayer-Vietoris sequence for class groups ⋮ Tensor products of irreducible integral \(p\)-adic representations of finite groups

Cites Work

• Unimodular integral circulants
• On matrix classes corresponding to an ideal and its inverse
• On the indecomposable representations of a finite group
• On the similarity transformation between a matrix and its transpose
• Modules of extensions over Dedekind rings
• Arithmetic of group representations
• Modules over finite groups
• The \(p\)-period of a finite group
• Behavior of integral group representations under ground ring extension
• Ideals in an extension field as modules over the algebraic integers in a finite number field
• Equivalence of representations under extensions of local ground rings
• Induced representations and projective modules
• Failure of the Krull-Schmidt theorem for integral representations
• On isomorphisms of orders
• Representations of cyclic groups in rings of integers. I
• Indecomposable representations of non-cyclic groups
• Indecomposable representations
• Projective modules over group rings and maximal orders
• Nil ideals in group rings
• Rings in which no fixed power of ideal classes becomes invertible
• A correspondence between classes of ideals and classes of matrices
• Remarks on Grothendieck rings
• A transfer theorem for modular representations
• The modular representation algebra of a finite group
• On representations of finite groups over valuation rings
• The integral representation ring of a finite group
• Integral representations of non-abelian groups of order pq
• Grothendieck groups of integral group rings
• On extensions of lattices
• Einige Bemerkungen über ganzzahlige Darstellungen endlicher Gruppen
• Group rings, semigroup rings and their radicals
• Relations between integral and modular representations
• Module extensions and blocks
• The trace map and separable algebras
• The number of generators of a module
• Group rings over Dedekind domains
• On the similarity transformation between an integral matrix with irreducible characteristic polynomial and its transpose
• Sur les ordres commutatifs avec un nombre fini de réseaux indecomposables
• Gruppenringe von unendlichem Darstellungstyp
• Darstellungen endlicher Gruppen in Polynomringen
• Some exact sequences in algebraic K-theory
• The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups
• Resolvents, discriminants, and trace invariants
• Maximal orders over Krull domains
• Genera and decompositions of lattices over orders
• Vertices and sources
• Isomorphic groups and group rings
• Multiplication in Grothendieck rings of integral group rings
• Galois cohomology of ambiguous ideals
• Finiteness of class numbers of representations of algebras over function fields
• Monomial representations under integral similarity
• Invariant rational functions and a problem of Steenrod
• Structure of semi-perfect hereditary noetherian rings
• An intertwining number theorem for integral representations and applications
• On modules of trivial cohomology over a finite group. I
• The ring of monomial representations. I: Structure theory
• On the Krull-Schmidt theorem for integral group representations of rank 1
• Representation rings
• Blocks of modular representations
• The Dedekind different and the homological different
• \(K\)-theory and stable algebra
• On the ubiquity of Gorenstein rings
• Projective modules over algebras
• On the theory of orders, in particular on the semigroup of ideal classes and genera of an order in an algebraic number field
• Ideal matrices. II
• Groups with a finite number of indecomposable integral representations
• Extensions of irreducible modules
• Ideal matrices. I
• The Grothendieck ring of a finite group
• Some indecomposable group representations
• Semisimple algebras over a commutative ring
• The maximal finite groups of \(4\times 4\) integral matrices
• Neuer Beweis der Endlichkeit der Klassenzahl bei unimodularer Äquivalenz endlicher ganzzahliger Substitutionsgruppen
• Über die Ausreduktion ganzzahliger Gruppendarstellungen bei arithmetischer Äquivalenz
• Indecomposable representations at characteristic \(p\)
• On the class number of non-maximal orders in $\mathfrak{p}$-adic division algebras
• On a generalization of the normal basis in abelian algebraic number fields
• A theorem on modules of trivial cohomology over a finite group
• Maschke Modules Over Dedekind Rings
• Residual Properties of Infinite Soluble Groups
• Relative Cohomology
• Integral Representations of Cyclic Groups of Prime Order
• TRIVIALITY OF VECTOR BUNDLES OVER THE AFFINE SPACE K ²
• Projective modules over finite groups
• On Representations of Orders Over Dedekind Domains
• Algebraic Vector Bundles Over the Product of an Affine Curve and the Affine Line
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers.
• Matrices of rational integers
• The Nonuniqueness of Irreducible Constituents of Integral Group Representations
• The Krull-Schmidt theorem for integral group representations
• On the semigroup of ideal classes in an order of an algebraic number field
• The Brauer Group of a Commutative Ring
• Torsion Free and Projective Modules
• On Projective Class Groups
• The module structure of Kummer extensions over Dedekind domains.
• On groups with finitely many indecomposable integral representations
• On the Class Number of Representations of an Order
• Integral Representations of Dihedral Groups of Order 2p
• Grothendieck Groups of Orders in Semisimple Algebras
• On the Structure of Group Algebras, I
• Nilpotent Elements in Rings of Integral Representations
• Rank Element of a Projective Module
• A Characterization of Group Rings as a Special Class of Hopf Algebras
• Decomposing Pairs of Modules
• Integral Representation Algebras
• On the Grothendieck Ring of an Abelian p-Group
• The Discriminant Matrices of An Algebraic Number Field
• Über die Geschlechter von Gittern über Ordnungen.
• Induction theorems for Grothendieck groups and Whitehead groups of finite groups
• The Integral Representation Ring a(R k G)
• Grothendieck groups of hereditary orders.
• Normal Bases in Galois Extensions of Number Fields
• On integral representations
• On relative Grothendieck rings
• On the Isomorphism of Integral Group Rings. I
• On the Irreducible Lattices of Orders
• Decomposition of Products of Modular Representations
• THE GROUPS OF UNITS OF THE INTEGRAL GROUP RINGS OF FINITE METABELIAN AND FINITE NILPOTENT GROUPS
• On Embedding of Lattices Belonging to the Same Genus
• Integral Group Rings of Finite Groups
• INVARIANTS FOR MODULES OVER COMMUTATIVE SEPARABLE ORDERS
• The Module Index and Invertible Ideals
• On the decomposition of modules
• On the semisimplicity of integral representation rings
• Indecomposable representations of finite groups over the ring of 𝑝-adic integers
• On Modules of Trivial Cohomology over a Finite Group, II (Finitely Generated Modules)
• Classes of Positive Definite Unimodular Circulants
• Submodules of Quaternion Algebras
• Hereditary Orders
• Structure of hereditary orders
• ON GROUP REPRESENTATIONS OVER A VALUATION RING
• Maximal Orders
• Integral Representations of the Direct Product of Groups
• On the Group Ring
• On Groups of Order p³
• Über die Hauptordnung eines Körpers als Gruppenmodul.
• The Units of Group-Rings
• Elementary Divisors and Modules
• Corrections and Supplementaries to My Paper concerning Krull-Remak-Schmidt’s Theorem
• On a Theorem of Latimer and Macduffee
• On Induced Representations of Groups
• Modules Over Dedekind Rings and Valuation Rings
• Classes of Matrices and Quadratic Fields (II)
• On -Adic Integral Representations of Finite Groups
• Matrices with finite period
• Induced and Produced Modules
• On Orders In Separable Algebras
• Classes of matrices and quadratic fields
• Algebraic \(K\)-theory
• Classes of matrices and quadratic fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A survey of integral representation theory