Related papers: The Generalized Flanders' Theorem in Unit-regular …

We give an elementary proof of a Caratheodory-type result on the invertibility of a sum of matrices, due first to Facchini and Barioli. The proof yields a polynomial identity, expressing the determinant of a large sum of matrices in terms…

Given an $n\times n$ matrix $c$ over a unitary ring $R$, the centralizer of $c$ in the full $n\times n$ matrix ring $M_n(R)$ is called a principal centralizer matrix ring, denoted by $S_n(c,R)$. We investigate its structure and prove: $(1)$…

Let R[G] be the group ring of a group G over an associative ring R with unity such that all prime divisors of orders of elements of G are invertible in R. If R is finite and G is a Chernikov (torsion FC-) group, then each R-derivation of…

In this note, we establish Andr\'{a}sfai--Erd\H{o}s--S\'{o}s-type stability theorems for two generalized Tur\'{a}n problems involving odd cycles, both of which are extensions of the Erd\H{o}s Pentagon Problem. Our results strengthen…

A class of $C^*$-algebras, to be called those of generalized tracial rank one, is introduced, and classified by the Elliott invariant. A second class of unital simple separable amenable $C^*$-algebras, those whose tensor products with…

In this paper, we study B-Fredholm elements in rings and algebras. After characterising these elements in terms of generalized Fredholm elements, we will give a condition on the socle of a unital primitive Banach algebra $A$, under which we…

We consider uniformly (DC) or periodically (AC) driven generalized infinite elastic chains (a generalized Frenkel-Kontorova model) with gradient dynamics. We first show that the union of supports of all the invariant measures, denoted by A,…

Let $\Gamma$ be a centerless irreducible higher rank arithmetic lattice in characteristic zero. We prove that if $\Gamma$ is either non-uniform or is uniform of orthogonal type and dimension at least 9, then $\Gamma$ is bi-interpretable…

We generalize the bounds on the inverses of diagonally dominant matrices obtained in [16] from scalar to block tridiagonal matrices. Our derivations are based on a generalization of the classical condition of block diagonal dominance of…

Inspired by the idea of Bernoulli decomposition, we give a simple proof for a generalization of Hal\'asz anti--concentration result about random sum of vectores in $\mathbb{R}^d$. From our results, we can give one upper bound for the…

We prove a general categorical theorem that enables us to state that under certain conditions, the range of a functor is large. As an application, we prove various results of which the following is a prototype: If every diagram, indexed by…

In this note, we investigate iterations of consistency, local and uniform reflection over $\mathbf{HA}$ (Heyting Arithmetic). In the case of uniform reflection, we give a new proof of Dragalin's extension of Feferman's completeness theorem…

We give a proof of the results of Chapuy and Douvropoulos [3] for irreducible spetsial reflection groups based on Deligne-Lusztig combinatorics. In particular, if f denotes the truncated Lusztig Fourier transform, we show that the image by…

Let k be a commutative ring. We find and characterize a new family of twisted planes (i. e. associative unitary k-algebra structures on the k-module k[X,Y], having k[X] and and k[Y] as subalgebras).Similar results are obtained for the…

We study Basic Arithmetic, BA introduced by W. Ruitenburg. BA is an arithmetical theory based on basic logic which is weaker than intuitionistic logic. We show that the class of the provably total recursive functions of BA is a proper…

The uniform Kruskal theorem extends the original result for trees to general recursive data types. As shown by A. Freund, M. Rathjen and A. Weiermann, it is equivalent to $\Pi^1_1$-comprehension, over $\mathsf{RCA_0}$ with the chain…

We define a generalization $\mathfrak{G}$ of the Grassmann algebra $G$ which is well-behaved over arbitrary commutative rings $C$, even when $2$ is not invertible. In particular, this enables us to define a notion of superalgebras that does…

For commutative rings, we introduce the notion of a {\em universal grading}, which can be viewed as the "largest possible grading". While not every commutative ring (or order) has a universal grading, we prove that every {\em reduced order}…

We propose a specific class of matrices which participate in factorization problems that turn to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or Yang-Baxter maps, expressed in non-commutative variables.…

We prove a reflection theorem, conjectured by Nakagawa and Ohno, for the number of quartic rings, or pairs of ternary quadratic forms, with a given cubic resolvent. Over $\mathbb{Z}$, our results are unconditional; we also allow the base to…