Related papers: A division's theorem on some class of $\mathcal{C}…

$\DeclareMathOperator{\Int}{Int} \DeclareMathOperator{\IntR}{Int{}^\text{R}} \newcommand{\Z}{{\mathbb Z}}$Let $D$ be a domain and let $\Int(D)$ and $\IntR(D)$ be the ring of integer-valued polynomials and the ring of integer-valued rational…

Let I be an m-primary ideal of a Noetherian local ring (R,m) of positive dimension. The coefficient $e_1(A)$ of the Hilbert polynomial of an I-admissible filtration A is called the Chern number of A. The Positivity Conjecture of Vasconcelos…

We develop the theory of groupoid graded semisimple rings. Our rings are neither unital nor one-sided artinian. Instead, they exhibit a strong version of having local units and being locally artinian, and we call them $\Gamma_0$-artinian.…

The semidirect product $\mathbb{G}=\mathbb{L}\rtimes \mathbb{K}$ attached to a compact-group action on a connected, simply-connected solvable Lie group has a dense set of compact elements precisely when the $s\in \mathbb{K}$ operating on…

Given a logarithmic analytic vector field $\partial$, we consider the formal ideal $B(\partial)$ defined by the collinearity locus of the semi-simple and nilpotent components of~$\partial$. Assuming that the eigenvalues of the linear part…

A unitary divisor $c$ of a positive integer $n$ is a positive divisor of $n$ that is relatively prime to $\displaystyle{\frac{n}{c}}$. For any integer $k$, the function $\sigma_k^*$ is a multiplicative arithmetic function defined so that…

In general the endomorphisms of a non-abelian group do not form a ring under the operations of addition and composition of functions. Several papers have dealt with the ring of functions defined on a group which are endomorphisms when…

Let $R$ be a standard graded algebra over an infinite field $\mathbb{K}$ and $M$ a finitely generated $\ZZ$-graded $R$-module. Let $I_1,\ldots I_m$ be graded ideals of $R$. The functions $r(M/I_1^{a_1}\ldots I_m^{a_m}M)$ and…

For a proper submodule $N$ of a finitely generated module $M$ over a Noetherian ring, the product of prime ideals which occur in a regular prime extension filtration of $M$ over $N$ is defined as its generalized prime ideal factorization in…

This paper is the second in a series of two papers about generalizing Quillen's Theorem A to strict $\infty$-categories. In the first one, we presented a proof of this Theorem A of a simplicial nature, direct but somewhat ad hoc. In the…

The main goal of this paper is the analytic classification of the germs of singular foliations generated, up to an analytic change of coordinates, by the germs of vector fields of form the…

For a discrete group $G$, we consider certain ideals $\mathcal{I}\subset c_0(G)$ of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C$^\ast$-algebra of $G$ and the C$^\ast$-completion…

We study commutants modulo some normed ideal of n-tuples of operators which satisfy a certain approximate unit condition relative to the ideal. We obtain results about the quotient of these Banach algebras by their ideal of compact…

The class of AD algebras of real rank zero is classified by an exact sequence of K-groups with coefficients, equipped with certain order structures. Such a sequence is always split, and one may ask why, then, the middle group is relevant…

Let $R$ be a commutative Noetherian ring, $N$ a finitely generated $R$-module and $I$ an ideal of $R$. The set $\bar{Q^*}(I, N)$, the quintasymptotic primes of $I$ with respect to $N$, was originally introduced by McAdam \cite{Mc2}. Also,…

We present the class of semi-admissible subsets of an open Riemann surface on which Carleman approximation by non-critical holomorphic functions is possible. In particular we characterize closed sets with empty interior on which continuous…

Let $H^\infty(\Delta)$ be the uniform algebra of bounded analytic functions on the open unit disc $\Delta$, and let $\mathfrak{M}(H^\infty)$ be the maximal ideal space of $H^\infty(\Delta)$. By regarding $\Delta$ as an open subset of…

We study the arithmetic of Galois-invariant sets of points on algebraic curves with controlled reduction behavior. Let $C$ be a smooth projective curve with a smooth proper model $\mathcal{C}$ over $\mathcal{O}_{K,S}$. We define $\Omega_n$…

It is well known that a domain without proper strongly divisorial ideals is completely integrally closed. In this paper we show that a domain without {\em prime} strongly divisorial ideals is not necessarily completely integrally closed,…

Ananyan and Hochster proved the existence of a function $\Phi(m,d)$ such that any graded ideal $I$ generated by $m$ forms of degree at most $d$ in a standard graded polynomial ring satisfies $\mathrm{reg}(I) \le \Phi(m,d)$. Relatedly,…