Generalized Matrix Rings Research Articles

Net subrings of generalized matrix rings

Let Λ be a ring with the following properties: (a) Λ is a direct sum of left ideals P1,..., Pn; (b) every nontrivial homomorphism Pi→Pj is a monomorphism; (c) for every i, j the intersection of any two submodules of Pj isomorphic to Pi contains a submodule isomorphic to Pi. Then Λ can be represented as a subring associated with a net of ideals in a generalized matrix ring. Bibliography: 5 titles.

Classical quotient rings of generalized matrix rings

An associative ring R with identity is a generalized matrix ring with idempotent set E if E is a finite set of orthogonal idempotents of R whose sum is 1. We show that, in the presence of certain annihilator conditions, such a ring is semiprime right Goldie if and only if eRe is semiprime right Goldie for all e ∈ E, and we calculate the classical right quotient ring of R.

Bergman's lemma for graded rings

We obtain a common generalization of Bergman's lemma on rings graded by finite groups and a result on generalized matrix rings due to Bergman and Jespers, Wauters

Rings of quotients of generalized matrix rings

Rings of quotients of generalized matrix rings

Injective dimension of generalized matrix rings

Injective dimension of generalized matrix rings

Maximal quotient rings of generalized matrix rings

Maximal quotient rings of generalized matrix rings