Rings of quotients

Quotients of Representation Rings

We give a proof using so-called fusion rings and q-deformations of Brauer algebras that the representation ring of an orthogonal or symplectic group can be obtained as a quotient of a ring Gr(O(∞)). This is obtained here as a limiting case for analogous quotient maps for fusion categories, with the level going to ∞. This in turn allows a detailed description of the quotient map in terms of a re...

Rings of Quotients of Rings of Functions

Computing in quotients of rings of integers

We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and their behavior under certain quotients. We illustrate the power of our ideas in a new modular normal form algorithm for modules over rings of integers, vastly o...

Quotients of Functors of Artin Rings

One of the fundamental problems in the study of moduli spaces is to give an intrinsic characterisation of representable functors of schemes, or of functors that are quotients of representable ones of some sort. Such questions are in general hard, leading naturally to geometry of algebraic stacks and spaces (see [1, 3]). On the other hand, in infinitesimal deformation theory a classical criterio...

Gaussian Properties of Total Rings of Quotients

In this paper we consider five possible extensions of the Prüfer domain notion to the case of commutative rings with zero divisors and relate the corresponding properties on a ring with the property of its total ring of quotients. We show that a Prüfer ring R satisfies one of the five conditions if and only if the total ring of quotients Q(R) of R satisfies that same condition. We focus in part...