Related papers: Generalized Jordan derivations on semiprime rings

The concepts of localizable set, localization of a ring and a module at a localizable set are introduced and studied. Localizable sets are generalization of Ore sets and denominator sets, and the localization of a ring/module at a…

Let E be an elementary abelian p-group of rank r and let k be a field of characteristic p. We introduce functors F_i from finitely generated kE-modules of constant Jordan type to vector bundles over projective space of dimension r-1. The…

The theory of complete generalized Jordan sets is employed to reduce the PDE with the irreversible linear operator $B$ of finite index to the regular problems. It is demonstrated how the question of the choice of boundary conditions is…

We study distributions on a Euclidean Jordan algebra V with values in a finite dimensional representation space for the identity component G of the structure group of V and homogeneous equivariance condition. We show that such distributions…

In this paper, we introduce and study e-injective semimodules, in particular over additively idempotent semirings. We completely characterize semirings all of whose semimodules are e-injective, describe semirings all of whose projective…

In this article, we first generalize Kaplansky's zero-divisor conjecture of group-rings $K[G]$ (with $K$ a field) to the more general setting of $G$-graded rings $R=\bigoplus\limits_{n\in G}R_{n}$ with $G$ a torsion-free group. Then we…

We define and explore in-depth the notion of {\it UQ rings} by showing their important properties and by comparing their behavior with that of the well-known classes of UU rings and JU rings, respectively. Specifically, among the other…

Continuing the study of the structure of semirings, we turn to the spectrum of prime congruences. Joo and Mincheva developed an elegant theory in the special case of idempotent semirings, which is generalized here to ``semiring pairs,''…

We describe non-trivial $\delta$-derivations of semisimple finite-dimensional Jordan algebras over an algebraically closed field of characteristic not 2, and of simple finite-dimensional Jordan superalgebras over an algebraically closed…

In this work, we study asymptotic zero distribution of random multi-variable polynomials which are random linear combinations $\sum_{j}a_jP_j(z)$ with i.i.d coefficients relative to a basis of orthonormal polynomials $\{P_j\}_j$ induced by…

Although there are many simple proofs of Jordan's decomposition theorem in the literature (see [1], the references mentioned there, and [2]), our proof seems to be even more elementary. In fact, all we need is the theorem on the dimensions…

A ring A is called presimplifiable if whenever a; b belongs to A and a = ab, then either a = 0 or b is a unit in A. Let A be a commutative ring and G be an abelian torsion group. For the group ring A[G], we prove that A[G] is…

A family of formal power series, such that its coefficients satisfy a recursion formula, is characterized in terms of the summability, in the sense of J. P. Ramis, of its elements along certain well chosen directions. We describe a set of…

We investigate some general machinery for describing semidualizing modules over generic constructions like ladder determinantal rings with coefficients in a normal domain. We also pose and investigate natural localization questions that…

As shown by Bonnaf\'e, a step in proving a Jordan decomposition of characters of finite special linear groups is the parametrization of unipotent characters of centralizers of semi-simple elements in projective linear groups. We show the…

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,…

In this article we prove several important results on graded rings, especially monoid-rings, that are motivated and inspired by Kaplansky's zero-divisor, unit and idempotents conjectures. Among the main results, we first generalize…

We prove a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces.

Let $\mathfrak{R}$ and $\mathfrak{R}'$ be two associative rings (not necessarily with the identity elements). A bijective map $\varphi$ of $\mathfrak{R}$ onto $\mathfrak{R}'$ is called a \textit{$m$-multiplicative isomorphism} if {$\varphi…

We introduce a lattice structure as a generalization of meet-continuous lattices and quantales. We develop a point-free approach to these new lattices and apply these results to $R$-modules. In particular, we give the module counterpart of…