Related papers: Infinite dimensional excellent rings
In this note we generalise a method of Perott to give new proofs that there are infinitely many prime numbers.
We prove explicit bounds for the number of sums of consecutive prime squares below a given magnitude.
We enumerate the 15768 perfect groups of order up to $2\cdot 10^6$, up to isomorphism, thus also completing the missing cases in the prior classification. The work supplements the by now well-understood computer classifications of solvable…
We exhibit a smooth complex rational affine surface with uncountably many nonisomorphic real forms.
We first establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. As applications, we exhibit several examples of additively idempotent semirings satisfying this condition, including a $4$-element…
Using Lie groupoids, we prove that the injectivity radius of a manifold with a Lie structure at infinity is positive.
We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.
We present new infinite arctangent sums and infinite sums of products of arctangents. Many previously known evaluations appear as special cases of the general results derived in this paper.
We prove that in normal rings the tight closure of an ideal can be computed as the sum of the ideal and a piece of the tight closure, called the special tight closure.
We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an extension.
We show that the rings of invariants for the three dimensional modular representations of an elementary abelian $p$-group of rank four are complete intersections with embedding dimension at most five. Our results confirm the conjectures of…
We show how tools from computational group theory can be used to prove that a subgroup of matrices has infinite index.
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case…
The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already in the…
In this note, we give a new nonexistence result of ternary extremal self-dual codes.
We prove some extensions of Andrews inequality.
We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.
In this note we consider the links of prime ideals of certain skew polynomial rings and prove our main theorem, namely theorem [5], which states the following.Let R be a noetherian ring that is link k-symmetric and let {\sigma} be an…
Suppose we are given black-box access to a finite ring R, and a list of generators for an ideal I in R. We show how to find an additive basis representation for I in poly(log |R|) time. This generalizes a quantum algorithm of Arvind et al.…