Related papers: A Note on Primitive Equivalence

A nonnegative matrix A is said to be primitive if there exists a positive integer m such that entries in A^m are positive and smallest such m is called the exponent of A: Primitive matrices are useful in the study of finite Markov chains…

This paper studies simplicity, primitivity and semiprimitivity of algebras associated to \'etale groupoids. Applications to inverse semigroup algebras are presented. The results also recover the semiprimitivity of Leavitt path algebras and…

Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…

We introduce the notion of primitive elements in arbitrary truncated $p$-divisible groups. By design, the scheme of primitive elements is finite and locally free over the base. Primitive elements generalize the "points of exact order $N$,"…

We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a…

Based on the fact that every finite-dimensional algebra over a field is isomorphic to the centralizer of \textbf{two} matrices, we approach the representation theory of finite-dimensional algebras over fields by centralizers of matrices.…

For any countable directed graph E we describe the primitive ideal space of the corresponding generalized Cuntz-Krieger algebra C*(E).

For a given selection of rows and columns from a Fourier matrix, we give a number of tests for whether the resulting submatrix is Hadamard based on the primitive sets of those rows and columns. In particular, we demonstrate that whether a…

In this article, we present a new method to study relative Cuntz-Krieger algebras for higher-rank graphs. We only work with edges rather than paths of arbitrary degrees. We then use this method to simplify the existing results about…

We give a simple and complete picture on the classification of relative Cuntz--Pimsner algebras (and so also of gauge-equivariant representations) using their intuitive parametrisation by kernel--covariance pairs.

Let $E$ be any directed graph, and $K$ any field. We classify those graphs $E$ for which the Leavitt path algebra $L_K(E)$ is primitive. As a consequence, we obtain classes of examples of von Neumann regular prime rings which are not…

We prove lower bounds of the form $\gg N/(\log N)^{3/2}$ for the number of primes up to $N$ primitively represented by a shifted positive definite integral binary quadratic form, and under the additional condition that primes are from an…

A nonnegative matrix $A$ is called primitive if $A^k$ is positive for some integer $k>0$. A generalization of this concept to finite sets of matrices is as follows: a set of matrices $\mathcal M = \{A_1, A_2, \ldots, A_m \}$ is primitive if…

Using the properties of the ideal of the coordinate Hermite interpolation on n-dimensional grid [4], we prove that the extension k in k[x1, x2, ..., xn] / (f1(x1), ..., fn(xn)) has a primitive element if and only if at most one of the…

In this article, we provide an explicit description of a set of generators for any ideal of an ultragraph Leavitt path algebra. We provide several additional consequences of this description, including information about generating sets for…

This paper begins the classification of all edge-primitive 3-arc-transitive graphs by classifying all such graphs where the automorphism group is an almost simple group with socle an alternating or sporadic group, and all such graphs where…

A factorization of a permutation into transpositions is called "primitive" if its factors are weakly ordered. We discuss the problem of enumerating primitive factorizations of permutations, and its place in the hierarchy of previously…

In this paper we will study integrability of distributions whose primitives are left regulated functions and locally or globally integrable in the Henstock--Kurzweil, Lebesgue or Riemann sense. Corresponding spaces of distributions and…

Let $R$ be a commutative unital ring, $\textsf{X}$ a subshift, and $\widetilde{\mathcal{A}}_R(\textsf{X})$ the corresponding unital subshift algebra. We establish the reduction theorem for $\widetilde{\mathcal{A}}_R(\textsf{X})$. As a…

A set of nonnegative matrices $\mathcal{M}=\{M_1, M_2, \ldots, M_k\}$ is called primitive if there exist indices $i_1, i_2, \ldots, i_m$ such that $M_{i_1} M_{i_2} \ldots M_{i_m}$ is positive (i.e. has all its entries $>0$). The length of…