Related papers: Some generalized Jordan maps on triangular rings f…

The additive monoid $R_+(x)$ is defined as the set of all nonnegative integer linear combinations of binomial coefficients $\binom{x}{n}$ for $n \in \mathbb Z_+$. This paper is concerned with the inquiry into the structure of $R_+(\alpha)$…

We study the interaction between the group law on an abelian variety and the additive structure induced on its image under a morphism to projective space. Let $A/F$ be a simple abelian variety, $f:A \rightarrow \mathbb{P}^n$ be a morphism…

We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.

We prove that every wandering Julia component of cubic rational maps eventually has at most two complementary components.

Let $K$ be a 2-torsion free ring with identity and $R_{n}(K,J)$ be the ring of all $n\times n$ matrices over $K$ such that the entries on and above the main diagonal are elements of an ideal $J$ of $K.$ We describe all Jordan derivations of…

This is the fifth in a series of articles devoted to showing that a typical covering map of large degree to a fixed, regular graph has its new adjacency eigenvalues within the bound conjectured by Alon for random regular graphs. In this…

Fix $k \ge 3$. If a multiplicative function $f$ satisfies \[ f(x_1+x_2+\dots+x_k) = f(x_1) + f(x_2) + \dots + f(x_k) \] for arbitrary positive triangular numbers $x_1, x_2, \dots, x_k$, then $f$ is the identity function. This extends Chung…

In this article, for generalized projective spaces with any weights, we prove four main theorems in three different contexts where the Unital Set Condition USC (Definition $2.8$) on ideals is further examined. In the first context we prove,…

The key result of this article is key lemma: if a Jordan curve $\gamma$ is invariant by a given C 1+$\alpha$ -diffeomorphism f of a surface and if $\gamma$ carries an ergodic hyperbolic probability $\mu$, then $\mu$ is supported on a…

We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with $n$ copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show…

Let $M_n$ be the algebra of $n \times n$ complex matrices and $\mathcal{T}_n \subseteq M_n$ the corresponding upper-triangular subalgebra. In their influential work, Petek and \v{S}emrl characterize Jordan automorphisms of $M_n$ and…

We show that each Jordan homomorphism $R\to R'$ of rings gives rise to a harmonic mapping of one connected component of the projective line over $R$ into the projective line over $R'$. If there is more than one connected component then this…

Let $A$ be a Banach algebra and $M$ be a Banach right $A$-module. A linear map $\delta : M\to M$ is called a generalized derivation if there exists a derivation $d : A \to A$ such that $$\delta(xa)=\delta(x)a + x d(a) \quad (a \in A, x \in…

We prove in this article the surjectivity of three maps. We prove in Theorem $1.6$ the surjectivity of the Chinese remainder reduction map associated to the projective space of an ideal with a given factorization into ideals whose radicals…

In this short note we prove that every Jordan derivation of triangular algebras is a derivation.

The goal of this paper is to generalize the theory of triangularizing matrices to linear transformations of an arbitrary vector space, without placing any restrictions on the dimension of the space or on the base field. We define a…

In the present paper we prove that every 2-local inner derivation on the matrix ring over a commutative ring is an inner derivation and every derivation on an associative ring has an extension to a derivation on the matrix ring over this…

We ask under what conditions on the function $f$, and a set of maps $\mathcal T$, it is the case that $f$ is a coboundary for some map in $\mathcal T$. We also consider for a function $f$, and a set of maps $\mathcal T$, when we have $f$…

We study the functional identity $G(x)f(x)=H(x)$ on a division ring $D$, where $f \colon D\to D$ is an additive map and $G(X)\ne 0, H(X)$ are generalized polynomials in the variable $X$ with coefficients in $D$. Precisely, it is proved that…

The dual of a map is a fundamental construction on combinatorial maps, but many other combinatorial objects also possess their notion of duality. For instance, the Tamari lattice is isomorphic to its order dual, which induces an involution…