Quotient categories and rings of quotient

Quotient Triangulated Categories

For self-orthogonal modules T , the quotient triangulated categories D(A)/K(addT ) are studied, in particular, their relations with the stable categories of some Frobenius categories are investigated. New descriptions of the singularity categories of Gorenstein algebras are obtained; and the derived categories of Gorenstein algebras are explicitly given, inside the stable categories of the grad...

Generalized Quotient Rings

Commuting probability for subrings and quotient rings

We prove that the commuting probability of a finite ring is no larger than the commuting probabilities of its subrings and quotients, and characterize when equality occurs in such a comparison.

Triangulated Categories of Gorenstein Cyclic Quotient Singularities

We prove there is an equivalence of derived categories between Orlov’s triangulated category of singularities for a Gorenstein cyclic quotient singularity and the derived category of representations of a quiver with relations, which is obtained from a McKay quiver by removing one vertex and half of the arrows. This result produces examples of distinct quivers with relations which have equivalen...

Commutative Rings with Finite Quotient Fields

We consider the class of all commutative reduced rings for which there exists a finite subset T ⊂ A such that all projections on quotients by prime ideals of A are surjective when restricted to T . A complete structure theorem is given for this class of rings, and it is studied its relation with other finiteness conditions on the quotients of a ring over its prime ideals. Introduction Our aim i...