Homological dimension and representation type of algebras under base field extension

DOI10.1007/BF01312441zbMath0498.16023MaRDI QIDQ1171116

Christian U. Jensen, Helmut Lenzing

Publication date: 1982

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/154868

zbMATH Keywords

separable field extensionfinite representation typefinite dimensional algebraself-injective dimensionfinitistic global dimension

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Separable extensions, Galois theory (12F10) Homological dimension in associative algebras (16E10) Ultraproducts and related constructions (03C20)

Related Items (23)

On Lie algebras associated with representation-directed algebras ⋮ Derived representation type and field extensions ⋮ A geometric approach to the finitistic dimension conjecture ⋮ Tame strongly simply connected algebras form an open scheme. ⋮ Centralizer matrix algebras and symmetric polynomials of partitions ⋮ Applications of model theory to representations of finite-dimensional algebras ⋮ Representations of a \(k\)-algebra over the rational functions over \(k\) ⋮ Left–right symmetry of finite finitistic dimension ⋮ A Footnote to the Multiplicative Basis Theorem ⋮ Essential dimension of representations of algebras ⋮ On the representation dimension of finite dimensional algebras ⋮ The pure-projective dimension of torsion-free divisible modules ⋮ Invariant properties of representations under excellent extensions. ⋮ Algebras that satisfy Auslander's condition on vanishing of cohomology. ⋮ Frobenius morphisms and representations of algebras ⋮ Applications of contravariantly finite subcategories ⋮ A homological approach to representations of algebras. I: The wild case ⋮ A non-commutative Bertini theorem ⋮ On tame strongly simply connected algebras ⋮ Auslander-Reiten sequences under base field extension ⋮ Representation-finite triangular algebras form an open scheme ⋮ Finitistic dimensions of finite dimensional monomial algebras ⋮ Tensor functors and finite representation type

Cites Work

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• On the free product of associative rings
• The Dimension of the Tensor Product of Two Field Extensions
• The Nullstellensatz and Tensor Products of Fields
• On the Dimension of Modules and Algebras, VIII. Dimension of Tensor Products

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