Related papers: Infinite dimensional excellent rings
We show that infinitely many cubic fields have class group of 2-rank 1.
It is shown that a finite monoid can have an infinite irredundant basis of equations.
We study etale extensions of rings that have FIP.
We compile a long list of equivalent formulations of Hilbert's Nullstellensatz in infinite dimensions, and prove a persistence result for the strong Nullstellensatz in large polynomial rings.
We produce an infinite family of imaginary quadratic fields whose ideal class groups have $3$-rank at least $2$.
Absolute integral closures of general commutative unital rings are explored. All rings admit absolute integral closures, but in general they are not unique. Among the reduced rings with finitely many minimal prime ideals, finite products of…
We consider random fields admitting a spectral representation with infinitely divisible integrator and prove some of their properties.
We study the ring extensions R \subseteq T having the same set of prime ideals provided Nil(R) is a divided prime ideal. Some conditions are given under which no such T exist properly containing R. Using idealization theory, the examples…
In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.
We consider rings whose one-sided ideals are close to automorphism-invariant modules. We study rings in which every (finitely generated) right ideal is automorphism invariant and rings in which every right ideal is a finite direct sum of…
Given a perfect valuation ring $R$ of characteristic $p$ that is complete with respect to a rank-$1$ nondiscrete valuation, we show that the ring $\mathbf{A}_{\text{inf}}$ of Witt vectors of $R$ has infinite Krull dimension.
We prove that the outer automorphism group of a free group of countably infinite rank is complete.
It is proven that, in any given base, there are infinitely many palindromic numbers having at most six prime divisors, each relatively large. The work involves equidistribution estimates for the palindromes in residue classes to large…
We describe a bound on the degree of the generators for some adjoint rings on surfaces and threefolds.
We provide infinitely many solutions of a Dirichlet problem on balls.
We introduce the notion of a Schur-finite element in a $\lambda$-ring.
A dynamical analog of the prime ideals for simple non-commutative rings is introduced. We prove a factorization theorem for the dynamical ideals. The result is used to classify the surface knots and links in the smooth 4-dimensional…
We show that good quotients of algebraic varieties with finitely generated Cox ring have again finitely generated Cox ring.
Let $R$ be local Noetherian ring of depth at least two. We prove that there are indecomposable $R$-modules which are free on the punctured spectrum of constant, arbitrarily large, rank.
We establish basic results on subrings of finite commutative rings and closely related rings. Among other applications we calculate the number of maximal subrings of a finite commutative local ring.