Related papers: Infinite dimensional excellent rings
We show that there is a strong minimal pair in the computably enumerable Turing degrees.
We characterize the commutative rings whose ideals (resp. regular ideals) are products of radical ideals.
We show that there exists a saturated graded ideal in a standard graded polynomial ring which has the largest total Betti numbers among all saturated graded ideals for a fixed Hilbert polynomial.
In this note a general result is proved that can be used to evaluate exactly a class of highly oscillatory integrals.
It is proved that spherically symmetric extermal black holes possess at least one external light ring. Our remarkably compact proof is based on the dominant energy condition which characterizes the external matter fields in the non-vacuum…
An infinite family of nonschurian separable association schemes is constructed.
We show that the group of holomorphic automorphisms of a Stein manifold X of dimension greater than 1 is infinite-dimensional, provided X is a homogeneous space of a holomorphic action of a complex Lie group.
It is shown that there exist infinitely many triangular numbers (congruent to 3 mod 12) which cannot be the distance between two perfect numbers.
It is proved that if $D$ is a $UFD$ and $R$ is a $D$-algebra, such that $U(R)\cap D\neq U(D)$, then $R$ has a maximal subring. In particular, if $R$ is a ring which either contains a unit $x$ which is not algebraic over the prime subring of…
Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like…
We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.
Necessary and sufficient conditions for a group to possess a faithful irreducible representation are investigated
We show that an infinite residually finite boundedly generated group has an infinite chain of finite index subgroups with ranks uniformly bounded, and give (sublinear) upper bounds on the ranks of arbitrary finite index subgroups of…
In this paper, we introduce the concept of graded extension dimension for a group graded ring R, denoted by gr.ext.dim(R). We prove that when R is strongly graded, its graded extension dimension coincides with the non-graded extension…
Starting with Zhang's theorem on the infinitude of prime doubles, we give an inductive argument that there exists an infinite number of prime $k$-tuples for at least one admissible set $\mathcal{H}_k=\{h_1,\ldots,h_k\}$ for each $k$.
We show that the big Ramsey degrees of every countable universal $u$-uniform $\omega$-edge-labeled hypergraph are infinite for every $u\geq 2$. Together with a recent result of Braunfeld, Chodounsk\'y, de Rancourt, Hubi\v{c}ka, Kawach, and…
Thirty years ago, Huneke (for local rings) and Lyubeznik (in general) conjectured that for all regular rings $R$, the local cohomology modules $H^i_I(R)$ have finitely many associated prime ideals. We prove substantial new cases of their…
We derive a linear estimate of the signature of positive knots, in terms of their genus. As an application, we show that every knot concordance class contains at most finitely many positive knots.
A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are…
We show that a suitable ring with a ``nice'' topology, in which convergent limits of units are units, is an \aleph_0-exchange ring. We generalize the argument to show that a semi-regular ring, R, with a ``nice'' topology, is a full exchange…