Sakurai, Taro

The Loewy structure of a module can be viewed as a q-analog of its composition factors. From this point of view we define q-composition multiplicity; q-composition length, and the q-Cartan matrix. By way of example, group algebras of finite p-groups and path algebras of finite acyclic quivers are investigated. Some known results for these algebras ...

Pei, Genhua Yin, Hongbo Zhang, Shunhua
Published in
Linear Algebra and Its Applications

Let A be a finite dimensional hereditary algebra over an algebraically closed field k, and let A(m) be the m-replicated algebra of A. In this paper, we investigate the structure properties of the endomorphism algebras of tilting modules of A(m), and prove that all the endomorphism algebras of tilting modules of A(m) can be realized as the iterated ...

Bremner, Murray R.
Published in
Linear Algebra and Its Applications

We use the computer algebra system Maple to study the 512-dimensional associative algebra QB3, the rational monoid algebra of 3×3 Boolean matrices. Using the LLL algorithm for lattice basis reduction, we obtain a basis for the radical in bijection with the 42 non-regular elements of B3. The center of the 470-dimensional semisimple quotient has dime...

Bremner, Murray R.
Published in
Linear Algebra and Its Applications

Pei, Genhua Yin, Hongbo Zhang, Shunhua
Published in
Linear Algebra and Its Applications

Chen, Hongxing Xi, Changchang
Published in
Forum Mathematicum

In this paper, we consider the endomorphism algebra of an infinitely generated tilting module of the form R𝒰 ⊕ R𝒰/R over a tame hereditary k-algebra R with k an arbitrary field, where R𝒰 is the universal localization of R at an arbitrary set 𝒰 of simple regular R-modules. We show that the derived module category of this endomorphism algebra is a re...

Li, Liping
Published in
Journal of Algebra

Li, Liping
Published in
Journal of Algebra

A finite EI category is a small category with finitely many morphisms such that every endomorphism is an isomorphism. They include finite groups, finite posets and free categories of finite quivers as special cases. In this paper we consider category algebras of finite EI categories with two or three objects, describe some criteria for finite repre...

Xiong, Bao-Lin Zhang, Pu Zhang, Yue-Hui
Published in
Forum Mathematicum

We generalize Ringel and Schmidmeier's theory on the Auslander–Reiten translation of the submodule category 𝒮 2 (A)$\mathcal {S}_2(A)$ to the monomorphism category 𝒮 n (A)$\mathcal {S}_n(A)$ ; the category consists of all chains of (n-1)$(n-1)$ composable monomorphisms of A-modules. As in the case of n=2$n=2$ , 𝒮 n (A)$\mathcal {S}_n(A)$ has Auslan...

Dugas, A. Huisgen-Zimmermann, B.

For any truncated path algebra Λ, we give a structural description of the modules in the categories $${\mathcal{P}^{