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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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