Related papers: Splittable Jordan homomorphisms and commutator ide…

Let $A$ and $B$ be associative algebras over a field $F$ with {\rm char}$(F)\ne 2$. Our first main result states that if $A$ is unital and equal to its commutator ideal, then every Jordan epimorphism $\varphi:A\to B$ is the sum of a…

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 $\mathcal{C}$ be a pocategory, $FI(\mathcal{C})$ the finitary incidence ring of $\mathcal{C}$ and $\varphi$ a Jordan isomorphism of $FI(\mathcal{C})$ onto an associative ring $A$. We study the problem of decomposition of $\varphi$ into…

By using a variation of a theorem on $n$-Jordan homomorphisms due to Herstein, we deduce the following G. An's result: Let $ A $ and $ B $ be two rings where $ A $ has a unit and $ char(B)> n. $ If every Jordan homomorphism from $ A $ into…

Let $A$ and $B$ be unital rings. An additive map $T:A\to B$ is called a weighted Jordan homomorphism if $c=T(1)$ is an invertible central element and $cT(x^2) = T(x)^2$ for all $x\in A$. We provide assumptions, which are in particular…

Let $\mathcal{I}(R)$ be the set of all ideals of a ring $R$, $\delta$ be an expansion function of $\mathcal{I}(R)$. In this paper, the $\delta$-$J$-ideal of a commutative ring is defined, that is, if $a, b\in R$ and $ab\in I\in…

We characterise all Jordan triple product homomorphisms, that is, mappings $\Phi$ satisfying $$ \Phi(ABA) = \Phi(A)\Phi(B)\Phi(A) $$ from the set of all Hermitian $n \times n$ complex matrices to the field of complex numbers. Further we…

In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…

We explore Jordan derivations of triangular matrices with entries from an additively idempotent semiring. The main result states that for any matrix A over additively idempotent semiring, if we put all the elements of the family of dense…

Let $P$ be a preordered set, $R$ a ring and $FI(P,R)$ the finitary incidence ring of $P$ over $R$. We find a criterion for all Jordan derivations of $FI(P,R)$ to be derivations and generalize Theorem 3.3 from arXiv:1411.6123. In particular,…

We determine all distant-isomorphisms between projective lines over semilocal rings. In particular, for those semisimple rings that do not have a simple component which is isomorphic to a field, every distant isomorphism arises from a…

Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…

We announce here a number of results concerning representation theory of the algebra $R=k<x,y>/ (xy-yx-y^2)$, known as Jordan plane (or Jordan algebra). We consider the question on 'classification' of finite-dimensional modules over 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…

Let $R$ be a commutative ring with unity $(1\not=0)$ and let $\mathfrak{J}(R)$ be the set of all ideals of $R$. Let $\phi:\mathfrak{J}(R)\rightarrow\mathfrak{J}(R)\cup\{\emptyset\}$ be a reduction function of ideals of $R$ and let…

Let $A$ and $B$ be commutative algebras and $n\geqslant 2$ an integer. Then each $n-$ Jordan homomorphism $h:A\rightarrow B$ is an $n-$homomorphism.

For commutative rings with identity, we introduce and study the concept of semi $r$-ideals which is a kind of generalization of both $r$-ideals and semiprime ideals. A proper ideal $I$ of a commutative ring $R$ is called semi $r$-ideal if…

We classify homotopes of classical symmetric spaces (studied in Part I of this work). Our classification uses the fibered structure of homotopes: they are fibered as symmetric spaces, with flat fibers, over a non-degenerate base; the base…

Let $R$ be a commutative ring with identity and let $I$ be an ideal of $R$. Let $R\Join I$ be the subring of $R\times R$ consisting of the elements $(r,r+i)$ for $r\in R$ and $i\in I$. We study the diameter and girth of the zero-divisor…

D. Benkovi\v{c} described Jordan homomorphisms of algebras of triangular matrices over a commutative unital ring without additive $2$-torsion. We extend this result to the case of noncommutative rings and remove the assumption of additive…