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Commutative graded- S -coherent rings

Anass Assarrar, Najib Mahdou, Ünsal Tekir, Suat Koç (2023)

Czechoslovak Mathematical Journal

Recently, motivated by Anderson, Dumitrescu’s S -finiteness, D. Bennis, M. El Hajoui (2018) introduced the notion of S -coherent rings, which is the S -version of coherent rings. Let R = ⨁ α ∈ G R α be a commutative ring with unity graded by an arbitrary commutative monoid G , and S a multiplicatively closed subset of nonzero homogeneous elements of R . We define R to be graded- S -coherent ring if every finitely generated homogeneous ideal of R is S -finitely presented. The purpose of this paper is to give the graded...

Componentwise injective models of functors to DGAs

Marek Golasiński (1997)

Colloquium Mathematicae

The aim of this paper is to present a starting point for proving existence of injective minimal models (cf. [8]) for some systems of complete differential graded algebras.

Differential calculus on almost commutative algebras and applications to the quantum hyperplane

Cătălin Ciupală (2005)

Archivum Mathematicum

In this paper we introduce a new class of differential graded algebras named DG ρ -algebras and present Lie operations on this kind of algebras. We give two examples: the algebra of forms and the algebra of noncommutative differential forms of a  ρ -algebra. Then we introduce linear connections on a  ρ -bimodule M over a  ρ -algebra  A and extend these connections to the space of forms from A to M . We apply these notions to the quantum hyperplane.

Ext-algebras and derived equivalences

Dag Madsen (2006)

Colloquium Mathematicae

Using derived categories, we develop an alternative approach to defining Koszulness for positively graded algebras where the degree zero part is not necessarily semisimple.

G r - ( 2 , n ) -ideals in graded commutative rings

Khaldoun Al-Zoubi, Shatha Alghueiri, Ece Y. Celikel (2020)

Commentationes Mathematicae Universitatis Carolinae

Let G be a group with identity e and let R be a G -graded ring. In this paper, we introduce and study the concept of graded ( 2 , n ) -ideals of R . A proper graded ideal I of R is called a graded ( 2 , n ) -ideal of R if whenever r s t ∈ I where r , s , t ∈ h ( R ) , then either r t ∈ I or r s ∈ G r ( 0 ) or s t ∈ G r ( 0 ) . We introduce several results concerning g r - ( 2 , n ) -ideals. For example, we give a characterization of graded ( 2 , n ) -ideals and their homogeneous components. Also, the relations between graded ( 2 , n ) -ideals and others that already exist, namely, the graded prime ideals,...

Graded blocks of group algebras with dihedral defect groups

Dusko Bogdanic (2011)

Colloquium Mathematicae

We investigate gradings on tame blocks of group algebras whose defect groups are dihedral. For this subfamily of tame blocks we classify gradings up to graded Morita equivalence, we transfer gradings via derived equivalences, and we check the existence, positivity and tightness of gradings. We classify gradings by computing the group of outer automorphisms that fix the isomorphism classes of simple modules.

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