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Phantom maps and purity in modular representation theory, I

D. Benson, G. Gnacadja (1999)

Fundamenta Mathematicae

Let k be a field and G a finite group. By analogy with the theory of phantom maps in topology, a map f : M → ℕ between kG-modules is said to be phantom if its restriction to every finitely generated submodule of M factors through a projective module. We investigate the relationships between the theory of phantom maps, the algebraic theory of purity, and Rickard's idempotent modules. In general, adding one to the pure global dimension of kG gives an upper bound for the number of phantoms we need...

P-injective group rings

Liang Shen (2020)

Czechoslovak Mathematical Journal

A ring $R$ is called right P-injective if every homomorphism from a principal right ideal of $R$ to $R_{R}$ can be extended to a homomorphism from $R_{R}$ to $R_{R}$ . Let $R$ be a ring and $G$ a group. Based on a result of Nicholson and Yousif, we prove that the group ring $RG$ is right P-injective if and only if (a) $R$ is right P-injective; (b) $G$ is locally finite; and (c) for any finite subgroup $H$ of $G$ and any principal right ideal $I$ of $RH$ , if $f \in {Hom}_{R} (I_{R}, R_{R})$ , then there exists $g \in {Hom}_{R} ({RH}_{R}, R_{R})$ such that ${g |}_{I} = f$ . Similarly, we also obtain equivalent characterizations...

Displaying 1 – 10 of 10

Phantom maps and purity in modular representation theory, I

P-injective group rings

Polynomial and transformation composition rings.

Primitive Ideals in Crossed Products and Rings with Finite Group Actions.

Primitive Ideals of Certain Noetherian Algebras.

Primitive Ideals of Group Algebras of Supersoluble Groups.

Primitive idempotents and the socle in group rings of periodic abelian groups

Primitive Idempotents of the Group Algebra CSL(3,q).

Primitivity in skew Laurent polynomial rings and related rings.

Projective modules over binary polyhedral groups.

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