Related papers: Infinite dimensional excellent rings

We give a construction of direct limits in the category of complete metric scalable groups and provide sufficient conditions for the limit to be an infinite-dimensional Carnot group. We also prove a Rademacher-type theorem for such limits.

The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains…

We prove that for all $n$, simultaneously, we can choose prime filtrations of $R/I^n$ such that the set of primes appearing in these filtrations is finite.

We identify an interesting special class of prime ideals in the finitary infinite symmetric group algebra. We show that the set of such ideals carries a semiring structure. Over the complex numbers, we establish a connection with spherical…

We prove there exist infinitely many inequivalent fusion categories whose Grothendieck rings do not admit any pseudounitary categorifications.

In this note, we present a new proof that the cyclotomic integers constitute the full ring of integers in the cyclotomic field.

We show that the Pythagoras number of rings of type $\mathbb{R}[x,y, \sqrt{f(x,y)}]$ is infinite, provided that the polynomial $f(x,y)$ satisfies some mild conditions.

Let R be a finite unitary ring whose group of units is not solvable but all groups of units of all its proper subrings are solvable. In this paper we classify these rings and show that all finite rings of order $p^n$ for $n < 5$ and some of…

We determine the arithmetical rank of every edge ideal of a Ferrers graph.

We prove that separable extensions of noetherian rings and finite \'etale morphisms of noetherian schemes give rise to separable extensions of singularity categories.

A well-known conjecture asserts that there are infinitely many primes $p$ for which $p - 1$ is a perfect square. We obtain upper and lower bounds of matching order on the number of pairs of distinct primes $p,q \le x$ for which $(p - 1)(q -…

We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and…

In this letter we prove existence and uniqueness of strong solutions to multi-dimensional SDEs with discontinuous drift and finite activity jumps.

This short paper gives another proof of the infinitude of primes by using upper box dimension, which is one of fractal dimensions.

We prove the existence of infinitely many real and imaginary fields whose 5-rank of the class group is >=3.

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals

We prove a result on lower bounds in large dimensions.

In this paper, we proved that there are infinite cube--free numbers of the form $[n^c]$ for any fixed real number $1<c<11/6$.

We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.

Infinite antichains of permutations have long been used to construct interesting permutation classes and counterexamples. We prove the existence and detail the construction of infinite antichains with arbitrarily large growth rates. As a…