A survey of integral representation theory
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Publication:5589399
DOI10.1090/S0002-9904-1970-12441-7zbMath0194.04701MaRDI QIDQ5589399
Publication date: 1970
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
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
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- 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
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