Related papers: Infinite dimensional excellent rings

We prove that nine-dimensional exceptional quotient singularities exist.

We prove that, for any $n\geq 0$, there exists an uncountable, $n$-dimensional, excellent, regular local ring with countable spectrum.

In this note, finite type epimorphisms of rings are characterized.

We proved that there are infinitely many pairs of twin prime.

We give an elementary proof of a result which is not as well known as it should be: a ring with a specified finite number of zero divisors is finite, with a precise bound on its order.

We proved that there are infinitely many cousin primes.

In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.

We give an explicit description of cubic rings over a discrete valuation ring, as well as a description of all ideals of such rings.

It has been a well-known fact since Euclid's time that there exist infinitely many rational primes. Two natural questions arise: In which other rings, sufficiently similar to the integers, are there infinitely many irreducible elements? Is…

We prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.

In this article it is proven the existence of integration of indefinite integrals as infinite derivative's series expansion. This also opens a new way to integrate a definite integral.

We prove completeness for the main examples of infinite-dimensional Lie groups and some related topological groups.

We prove Dirichlet's theorem for polynomial rings: Let F be a pseudo algebraically closed field. Then for all relatively prime polynomials a(X), b(X)\in F[X] and for every sufficiently large positive integer n there exist infinitely many…

In this paper, we give a detailed proof to a result of Gabber (unpublished) on the lifting problem of quasi-excellent rings, extending the previous work on Nishimura-Nishimura. As a corollary, we establish that an ideal-adic completion of…

In the present note, we will show that there are infinitely many composite twisted torus knots.

In this paper we investigate complex dynamics in infinite dimensions.

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

We describe derivations of several important associative and Lie rings of infinite matrices over general rings of coefficients.

We find necessary and sufficient conditions for the finite separability of finitely generated commutative rings. Namely, we prove that every such ring is a finite extension of its torsion ideal $I_k$ where $k$ is square-free, and $I_k$ is a…

We show that the class of completely m-full ideals coincides with the class of componentwise linear ideals in a polynomial ring over an infinite field.