Larki, Hossein
Published in
Forum Mathematicum

Given any finitely aligned higher-rank graph Λ and any unital commutative ring R, the Kumjian–Pask algebra KP R ( Λ ) {\mathrm{KP}_{R}(\Lambda)} is known as the higher-rank generalization of Leavitt path algebras. After the characterization of simple Kumjian–Pask algebras by Clark and Pangalela among others, in this article we focus on the purely...

Al-Zoubi, Khaldoun Al-Qderat, Amani
Published in
Open Mathematics

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper we will obtain some results concerning the graded comultiplication modules over a commutative graded ring.

Al-Zoubi, Khaldoun Al-Dolat, Mohammed
Published in
Advances in Pure and Applied Mathematics

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded classical primary submodules. Various properties of graded classical primary submodules are considered.

Holdaway, Cody Sisodia, Gautam
Published in
Journal of Algebra

Let k be a field, Q a finite directed graph, and kQ its path algebra. Make kQ an N-graded algebra by assigning each arrow a positive degree. Let I be an ideal in kQ generated by a finite number of paths and write A=kQ/I. Let QGrA denote the quotient of the category of graded right A-modules modulo the Serre subcategory consisting of those graded mo...

Dăscălescu, S. Năstăsescu, C. Năstăsescu, L.
Published in
Journal of Algebra

CAO, Haijun LI, Fang ZHANG, Mianmian
Published in
Acta Mathematica Scientia

Dăscălescu, S. Năstăsescu, C. Năstăsescu, L.
Published in
Journal of Algebra

We consider Frobenius algebras in the monoidal category of right comodules over a Hopf algebra H. If H is a group Hopf algebra, we study a more general Frobenius type property, uncover the structure of graded Frobenius algebras, and investigate graded symmetric algebras. The graded Frobenius concept is related to Frobenius functors.

Holdaway, Cody Sisodia, Gautam
Published in
Journal of Algebra

CAO, Haijun LI, Fang ZHANG, Mianmian
Published in
Acta Mathematica Scientia

The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra from a Clifford monoid S = [Y;Gα, φα,β] by Ore-extensions, and to obtain a co-Frobenius semilattice graded weak Hopf algebra H(S, n, c, χ, a, b) through factoring At by a semilattice graded weak Hopf ideal.

Nystedt, Patrik Öinert, Johan

For an extension A/B of neither necessarily associative nor necessarily unital rings, we investigate the connection between simplicity of A with a property that we call A-simplicity of B. By this we mean that there is no non-trivial ideal I of B being A-invariant, that is satisfying AI \subseteq IA. We show that A-simplicity of B is a necessary con...