Related papers: Commuting Jordan derivations on triangular rings a…

We address a Jordan version of Johnson theorem on (associative) algebras of quotients, namely whether a strongly nonsingular (the Jordan version of nonsingularity) has a von Neumann regular algebra of quotients. Although the answer is…

We consider a rank one group $G = \langle A,B \rangle $ which acts cubically on a module $V$, this means $[V,A,A,A] =0$ but $[V,G,G,G] \ne 0$. We have to distinguish whether the group $A_0 :=C_A([V,A]) \cap C_A(V/C_V(A))$ is trivial or not.…

We study the conformal groups of Jordan algebras along the lines suggested by Kantor. They provide a natural generalization of the concept of conformal transformations that leave 2-angles invariant to spaces where "p-angles" can be defined.…

For a geometrically rational surface X over an arbitrary field of characteristic different from 2 and 3 that contains all roots of 1, we show that either X is birational to a product of a projective line and a conic, or the group of…

We study the case when solution of an ODE at a given initial condition fail to be unique and investigate what are the possible time-1 sections of the `solution funnel'. Along the way we give construction of a natural complete metric on the…

Determining the Jordan canonical form of the tensor product of Jordan blocks has many applications including to the representation theory of algebraic groups, and to tilting modules. Although there are several algorithms for computing this…

Jordan-Wigner-type transformations connecting the spin-3/2 operators and two kinds of fermions are derived. A general condition of fermionizability of spins is obtained and a theorem establishing connection between half integer spins and…

Let $A$ be a finite-dimensional algebra over a field $F$ with char$(F)\ne 2$. We show that a linear map $D:A\to A$ satisfying $xD(x)x\in [A,A]$ for every $x\in A$ is the sum of an inner derivation and a linear map whose image lies in the…

An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one (essentially different) factorization into irreducibles. In the case of the ring $\text{Int}(D)=\{f\in K[x]\mid f(D)\subseteq D\}$,…

We describe the structure of all continuous Jordan triple endomorphisms of the set $\mathbb{P}_2$ of all positive definite $2\times 2$ matrices thus completing a recent result of ours. We also mention an application concerning sorts of…

We introduce a complete radical formula for modules over non-commutative rings which is the equivalence of a radical formula in the setting of modules defined over commutative rings. This gives a general frame work through which known…

Given a certain factorization property of a ring $R$, we can ask if this property extends to the polynomial ring over $R$ or vice versa. For example, it is well known that $R$ is a unique factorization domain if and only if $R[X]$ is a…

Let $K$ be a 2-torsion free ring with identity. We give a description of the Lie derivations of $R=R_{n}(K,J)=NT_{n}(K)+M_{n}(J)$, the ring of all $n\times n$ matrices over $K$ such that the entries on and above the main diagonal are…

We show that automorphism groups of Moishezon threefolds are always Jordan.

We compute the Jordan constant for the group of birational automorphisms of a projective plane $\mathbb{P}^2_{\mathbb k}$, where ${\mathbb k}$ is either an algebraically closed field of characteristic 0, or the field of real numbers, or the…

In this paper, we introduce multiplicative semiderivation and we investigate the commutativity of semiprime rings satisfying certain conditions and identities involving multiplicative semiderivations on a nonzero ideal I of a ring R.

Let $\R$ be an alternative ring containing a nontrivial idempotent and $\D$ be a multiplicative Lie-type derivation from $\R$ into itself. Under certain assumptions on $\R$, we prove that $\D$ is almost additive. Let $p_n(x_1, x_2, \cdots,…

Let $M_n$ be the algebra of $n \times n$ complex matrices. We consider arbitrary subalgebras $\mathcal{A}$ of $M_n$ which contain the algebra of all upper-triangular matrices (i.e.\ block upper-triangular subalgebras), and their Jordan…

Let $RG$ denote the group ring of the torsion group $G$ over a commutative ring $R$ with identity. In this paper we present proofs of some statements that appear without to be proved in the literature. We establish the valid implications…

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…