We take an algorithmic and computational approach to a basic problem in abstract algebra: determining the correct generalization to dialgebras of a given variety of nonassociative algebras. We give a simplified statement of the KP algorithm introduced by Kolesnikov and Pozhidaev for extending polynomial identities for algebras to corresponding identities for dialgebras. We apply the KP algorith...

In a recent article [8], Gowda and Sznajder studied the concept of Schur complement in Euclidean Jordan algebras and described Schur determinantal and Haynsworth inertia formulas. In this article, we establish some more results on the Schur complement. Specifically, we prove, in the setting of Euclidean Jordan algebras, an analogue of the Crabtree-Haynsworth quotient formula and show that any S...

In this paper we shall study the multipliers on Banach algebras and We prove some results concerning Arens regularity and amenability of the Banach algebra M(A) of all multipliers on a given Banach algebra A. We also show that, under special hypotheses, each Jordan multiplier on a Banach algebra without order is a multiplier. Finally, we present some applications of m...

Let $mathcal{H}$ and $mathcal{K}$ be infinite dimensional Hilbert spaces, while $mathcal{B(H)}$ and $mathcal{B(K)}$ denote the algebras of all linear bounded operators on $mathcal{H}$ and $mathcal{K}$, respectively. We characterize the forms of additive mappings from $mathcal{B(H)}$ into $mathcal{B(K)}$ that preserve the nonzero idempotency of either Jordan products of operators or usual produc...

Let A be a unital algebra and M be a unital A-bimodule. A characterization of generalized derivations and generalized Jordan derivations from A into M, through zero products or zero Jordan products, is given. Suppose that M is a unital left A-module. It is investigated when a linear mapping from A into M is a Jordan left derivation under certain conditions. It is also studied whether an algebra...

A recent paper by N. Jacobson' develops a theory of Jordan algebras with minimum condition which is similar to the associative theory of semisimple Artinian rings. Jacobson shows that any algebra satisfying his axioms is a direct sum of a finite number of simple algebras satisfying his axioms, and he deduces the structure of those simple algebras which contain three mutually orthogonal idempote...