24 citations · 27 across the 15 of their papers we have counts for
10 papers · 1 filter
A linear algebra approach to graded Frobenius algebras
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu +1
If is a finite-dimensional algebra graded by a group , and , we define a variant of paratrophic matrix associated with and , and we use it to characterize the…
Graded Frobenius algebras from tensor algebras of bimodules
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
We consider certain quotient algebras of tensor algebras of bimodules over a finite-dimensional algebra , and we investigate Frobenius type properties of such algebras. Our…
Picard groups of quasi-Frobenius algebras and a question on Frobenius strongly graded algebras
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
Our initial aim was to answer the question: does the Frobenius (symmetric) property transfers from a strongly graded algebra to its homogeneous component of trivial degree? Related…
Graded Frobenius Rings
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter…
Symmetric algebras of corepresentations and smash products
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
We investigate Frobenius algebras and symmetric algebras in the monoidal category of right comodules over a Hopf algebra ; for the symmetric property is assumed to be cosove…
Graded semisimple algebras are symmetric
Sorin Dascalescu, Constantin Nastasescu, Laura Nastasescu
We study graded symmetric algebras, which are the symmetric monoids in the monoidal category of vector spaces graded by a group. We show that a finite dimensional graded semisimple…
Quasi-Frobenius functors. Applications
F. Castano Iglesias, C. Nastasescu, J. Vercruysse
We investigate functors between abelian categories having a left adjoint and a right adjoint that are \emph{similar} (these functors are called \emph{quasi-Frobenius functors}). We…
Localization in coalgebras. Applications to finiteness conditions
J. Gomez-Torrecillas, C. Nastasescu, B. Torrecillas
The injective right comodules appearing in the minimal injective resolution of a finite-dimensional comodule need not to be of finite dimension or even quasi-finite. The obstructio…
Wide Morita contexts, relative injectivity and equivalence results
N. Chifan, S. Dascalescu, C. Nastasescu
We extend Morita theory to abelian categories by using wide Morita contexts. Several equivalence results are given for wide Morita contexts between abelian categories, widely exten…
On gradings of matrix algebras and descent theory
S. Caenepeel, S. Dăscălescu, C. Năstăsescu
We classify gradings on matrix algebras by a finite abelian group. A grading is called good if all elementary matrices are homogeneous. For cyclic groups, all gradings on a matrix…