Related papers: On factorization of elements in Pimenov algebras

We show that all twist knots, certain double twist knots and some other 2-bridge knots are minimal elements for the partial ordering on the set of prime knots. The key to these results are presentations of their character varieties using…

We give explicit formulae for certain elements occurring in the Bernstein presentation of an affine Hecke algebra, in terms of the usual Iwahori- Matsumoto generators. We utilize certain minimal expressions for said elements and we give a…

We give a classification of semisimple and separable algebras in a multi-fusion category over an arbitrary field in analogy to Wedderben-Artin theorem in classical algebras. It turns out that, if the multi-fusion category admits a…

We show that every algebraic group scheme over a field with at least 8 elements can be realized as the group of automorphisms of a nonassociative algebra. This is only a modest improvement of the theorem of Gordeev and Popov (2003), but it…

We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct…

A partial order on the set of prime knots can be defined by the existence of an epimorphism between knot groups. We prove that all the prime knots with up to $6$ crossings are minimal. We also show that each fibered knot with the…

The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…

The groups distinguish their von Neumann algebras, in the case when these are factors.

Suppose we wish to embed an (associative) $k$-algebra $A$ in a $k$-algebra $R$ generated in some specified way; e.g., by two elements, or by copies of given $k$-algebras $A_1,$ $A_2,$ $A_3.$ Several authors have obtained sufficient…

A simple sufficient condition for certain cyclic algebras of odd degree d to be split is presented. It employs certain binary forms of degree d and the values they represent. A similar sufficient condition for certain Albert algebras not to…

We present algorithms to factorize weighted homogeneous elements in the first polynomial Weyl algebra and $q$-Weyl algebra, which are both viewed as a $\mathbb{Z}$-graded rings. We show, that factorization of homogeneous polynomials can be…

We develop an elementary theory of partially additive rings as a foundation of ${\mathbb F}_1$-geometry. Our approach is so concrete that an analog of classical algebraic geometry is established very straightforwardly. As applications, (1)…

Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…

We give the classification of subfactor planar algebras at index exactly 5. All the examples arise as standard invariants of subgroup subfactors. Some of the requisite uniqueness results come from work of Izumi in preparation. The…

We generalize the existence of maximal orders in a semi-simple algebra for general ground rings. We also improve several statements in Chapter 5 and 6 of Reiner's book concerning separable algebras by removing the separability condition,…

Given an initial family of sets, we may take unions, intersections and complements of the sets contained in this family in order to form a new collection of sets; our construction process is done recursively until we obtain the last family.…

The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types of the groups…

In this article, we prove some factorization results for several classes of polynomials having integer coefficients, which in particular yield several classes of irreducible polynomials. Such classes of polynomials are devised by imposing…

A necessary and sufficient condition for an element of an algebra (in the sense of Universal Algebra) to be in the dominion of a subalgebra is given, in terms of transferable sets. This criterion is then used to formulate a more wieldy…

A group $G$ is said to be factorized into subsets $A_1, A_2, \ldots, A_s\subseteq G$ if every element $g$ in $G$ can be uniquely represented as $g=g_1g_2\ldots g_s$, where $g_i\in A_i$, $i=1,2,\ldots,s$. We consider the following…