A functional equation for quadratic forms.
A functional treatment of right invariant holoids.
A functor between categories of regular modules for wild hereditary algebras.
A functor-valued invariant of tangles.
A -minimal model for principal -bundles
Sullivan associated a uniquely determined to any simply connected simplicial complex . This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space . In case is the total space of a principal -bundle, ( is a compact connected Lie-group) we associate a -equivariant model , which is a collection of “-homotopic” ’s with -action. will, in general, be different from the Sullivan’s minimal model of the space . contains the total rational...
A general concept of the pseudoprojective module
A general form of non-Frobenius self-injective algebras
Applying the classical work of Nakayama [Ann. of Math. 40 (1939)], we exhibit a general form of non-Frobenius self-injective finite-dimensional algebras over a field.
A General Injectivity for Modules.
A general theory of Fountain-Gould quotient rings
A generalisation of Amitsur's A-polynomials
We find examples of polynomials whose eigenring is a central simple algebra over the field .
A Generalisation of Swan's Theorem.
A generalization of a theorem of Faith and Menal and applications.
A Generalization of Baer's Lemma
There is a classical result known as Baer’s Lemma that states that an -module is injective if it is injective for . This means that if a map from a submodule of , that is, from a left ideal of to can always be extended to , then a map to from a submodule of any -module can be extended to ; in other words, is injective. In this paper, we generalize this result to the category consisting of the representations of an infinite line quiver. This generalization of Baer’s Lemma...
A generalization of Eichler's trace formula.
Eichler's trace formula for traces of the Brandt-Eichler matrices is proved for arbitrary totally definite orders in central simple algebras of prime index over global fields. A formula for type numbers of such orders is proved as an application.
A generalization of Mathieu subspaces to modules of associative algebras
We first propose a generalization of the notion of Mathieu subspaces of associative algebras , which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to -modules . The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets σ(N) and τ(N) of stable...
A generalization of the Auslander transpose and the generalized Gorenstein dimension
Let be a left and right Noetherian ring and a semidualizing -bimodule. We introduce a transpose of an -module with respect to which unifies the Auslander transpose and Huang’s transpose, see Z. Y. Huang, On a generalization of the Auslander-Bridger transpose, Comm. Algebra 27 (1999), 5791–5812, in the two-sided Noetherian setting, and use to develop further the generalized Gorenstein dimension with respect to . Especially, we generalize the Auslander-Bridger formula to the generalized...
A Generalization of the Lambda Algebra.
A generalization of the prime radical of an ideal.
A generalization of Ulm subgroups
A generalized Picard group for prime rings