Finiteness conditions and infinite matrix rings

Schur-finiteness in Λ-rings

We introduce the notion of a Schur-finite element in a λ-ring. Since the beginning of algebraic K-theory in [G57], the splitting principle has proven invaluable for working with λ-operations. Unfortunately, this principle does not seem to hold in some recent applications, such as the K-theory of motives. The main goal of this paper is to introduce the subring of Schur-finite elements of any λ-r...

Finiteness of Unramified Deformation Rings

We prove that the universal unramified deformation ring R of a continuous Galois representation ρ : GF+ → GLn(k) (for a totally real field F and finite field k) is finite over O = W (k) in many cases. We also prove (under similar hypotheses) that the universal deformation ring R is finite over the local deformation ring R.

Differential Polynomial Rings of Triangular Matrix Rings

Correspondence Functors and Finiteness Conditions

We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties which do not hold for other types of functors. In particular, if k is a field and if F is a correspondence functor, then F is finitely generate...

A commutativity-or-finiteness condition for rings

In view of this result, it was conjectured that any ring with only finitely many noncentral subrings is either finite or commutative. It is our principal goal to prove this conjecture; and in the process we provide a new proof of Theorem 1.1. For any ring R, the symbols N, D, Z , and ℘(R) will denote, respectively, the set of nilpotent elements, the set of zero divisors, the center, and the pri...