Related papers: Unique prime factorization for infinite tensor pro…

In this paper we study modular extendability and equimodularity of endomorphisms and E$_0$-semigroups on factors with respect to f.n.s. weights. We show that modular extendability is a property that does not depend on the choice of weights,…

A necessary condition for uniqueness of factorizations of elements of a finite group $G$ with factors belonging to a union of some conjugacy classes of $G$ is given. This condition is sufficient if the number of factors belonging to each…

We prove a variety results on tensor product factorizations of finite dimensional Hopf algebras (more generally Hopf algebras satisfying chain conditions in suitable braided categories). The results are analogs of well-known results on…

Define the $n$-th fibotomic polynomial to be the product of the monic irredicible factors of the $n$-th Fibonacci polynomial which are not factors of any Fibonacci polynomial of smaller degree. In this paper, we prove a number of properties…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…

This paper addresses a conjecture of Kadison and Kastler that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent to each sufficiently close von Neumann algebra N and, moreover, the implementing unitary can be chosen…

This paper is concerned with the prime spectrum of a tensor product of algebras over a field. It seeks necessary and sufficient conditions for such a tensor product to have the S-property, strong S-property, and catenarity. Its main results…

We prove that if $\Gamma$ is an icc irreducible lattice in a product of connected non-compact rank one simple Lie groups with finite center, then the II$_1$ factor $L(\Gamma)$ is prime. In particular, we deduce that the II$_1$ factors…

The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor…

We show that any finite-entropy, countable-valued finitary factor of an i.i.d process can also be expressed as a finitary factor of a finite-valued i.i.d process whose entropy is arbitrarily close to the target process. As an application,…

We construct, for every prime p, a function field K of characteristic p and an ordinary abelian variety A over K, with no isotrivial factors, that admits an etale self-isogeny of p-power degree. As a consequence, we deduce that there exist…

We show that each member of a doubly infinite sequence of highly nonlinear expressions of Bernoulli polynomials, which can be seen as linear combinations of certain higher-order convolutions, is a multiple of a specific product of linear…

Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that for $\alpha\in\mathbb{R}\backslash\mathbb{Q},\,\beta\in\mathbb{R}$ and $0<\theta<10/1561$, there…

We develop first steps in the study of factorizations of elements in ultraproducts of commutative cancellative monoids into irreducible elements. A complete characterization of the (multi-)sets of lengths in such objects is given. As…

We show that a number of key structural properties transfer between sufficiently close II$_1$ factors, including solidity, strong solidity, uniqueness of Cartan masas and property $\Gamma$. We also examine II$_1$ factors close to tensor…

We show the existence of noncommutative random variables with finite free entropy but which do not generate a free group factor.

We provide a family of group measure space II_1 factors for which all finite index subfactors can be explicitly listed. In particular, the set of all indices of irreducible subfactors can be computed. Concrete examples show that this index…

We show that the tensor product $M \mathbin{\overline{\otimes}} N$ of any two full factors $M$ and $N$ (possibly of type ${\rm III}$) is full and we compute Connes' invariant $\tau(M \mathbin{\overline{\otimes}} N)$ in terms of $\tau(M)$…

Prime factorization is an outstanding problem in arithmetic, with important consequences in a variety of fields, most notably cryptography. Here we employ the intriguing analogy between prime factorization and optical interferometry in…

A complete determination of the prime ideals invariant under winding automorphisms in the generic 3 by 3 quantum matrix algebra is obtained. Explicit generating sets consisting of quantum minors are given for all of these primes, thus…