Related papers: Jordan derivations on triangular matrix rings

Let $J$ be the Jacobian of a smooth projective complex curve $C$ which admits non-trivial automorphisms, and let $A(J)$ be the ring of algebraic cycles on $J$ with rational coefficients modulo algebraic equivalence. We present new…

We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has a continuous or homeomorphic extension to the closures of the domains. Our conditions involve the…

Let $B \subseteq A$ be an extension of finite dimensional algebras. We provide a sufficient condition for the existence of triangle equivalences of singularity categories (resp. Gorenstein defect categories) between $A$ and $B$. This result…

We recognise Harada's generalized categories of diagrams as a particular case of modules over a monad defined on a finite direct product of additive categories. We work in the dual (albeit formally equivalent) situation, that is, with…

Let $\mathcal{R}$ be a commutative ring with identity, $I(X,\mathcal{R})$ be the incidence algebra of a locally finite pre-ordered set $X$. In this note, we characterise the derivations of $I(X,\mathcal{R})$ and prove that every Jordan…

In this paper, we mainly study a class of biderivations and triple homomorphisms on perfect Jordan algebras. Let $J$ be a Jordan algebra and $\delta :J \times J \rightarrow J$ a symmetric biderivation satisfying $\delta(w , u \circ v) = w…

We compute an analogue of Pascal's triangle enriched in bilinear forms over a finite field. This gives an arithmetically meaningful count of the ways to choose $j$ ring homomorphisms into an algebraic closure from an \'etale extension of…

Let $k$ be a field of arbitrary characteristic, $A$ be a domain and $K=\mathrm{frac}(A)$. Then (1) All exponential maps of $k^{[3]}$ are rigid, and we give a necessary and sufficient condition for the triangularity of $\delta \in…

Let N be a left near ring. A map d on N is called a nonzero multiplicative derivation if d(xy)=xd(y)+d(x)y holds for all x,y elements of N.In the present paper, we shall extend some well known results concerning commutativity of prime rings…

Determinants of structured matrices play a fundamental role in both pure and applied mathematics, with wide-ranging applications in linear algebra, combinatorics, coding theory, and numerical analysis. In this work, the enumeration of…

The Lang map, namely the universal dominant rational map to a variety of general type, is constructed and briefly discussed in relation with arithmetic conjectures of Harris, Lang and Manin. Existence of the Lang map follows from the…

We study holomorphic maps between C$^*$-algebras $A$ and $B$. When $f:B_A (0,\varrho) \longrightarrow B$ is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball $U=B_{A}(0,\delta)$ and we assume…

In this paper, we classify Jordan superalgebras of dimension up to three over an algebraically closed field of characteristic different of two. Our main motivation to obtain such classification comes out from the intention to give an answer…

Following Mitchell's philosophy, in this paper we define the analogous of the triangular matrix algebra to the context of rings with several objects. Given two additive categories $\mathcal{U}$ and $\mathcal{T}$ and $M\in…

Let $\mathcal{A}=(A_{1},...,A_{n},...)$ be a finite or infinite sequence of $2\times2$ matrices with entries in an integral domain. We show that, except for a very special case, $\mathcal{A}$ is (simultaneously) triangularizable if and only…

The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…

We give an improved polynomial bound on the complexity of the equation solvability problem, or more generally, of finding the value sets of polynomials over finite nilpotent rings. Our proof depends on a result in additive combinatorics,…

Within the framework of Berwald-Moor Geometry in H_3, the paper studies the construction of additive poly-angles (bingles and tringles). It is shown that, considering additiveness in the large, there exist an infinity of such poly-angles.

Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: For every circle the multi-ratio of its six intersection points with neighboring circles is equal to -1.…

Associating to each pre-order on the indices 1,...,n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n x n matrix rings. Rings within the order-convex hull of…