Velásquez and Felipe recently introduced quasi-Jordan algebras based on the product a / b = 1 2 (a a b + b ` a) in an associative dialgebra with operations a and `. We determine the polynomial identities of degree ≤ 4 satisfied by this product. In addition to right commutativity and the right quasi-Jordan identity, we obtain a new associator-derivation identity. Loday [1, 2] defined an (associa...

Given an associative algebra satisfying the left commutativity identity abc = bac (Perm-algebra) with a derivation d, new operation a°b=ad(b) is left-symmetric (pre-Lie). We derive necessary and sufficient conditions for to be embeddable into differential Perm-algebra.

We have isolated a 1595-bp transposable element from the multicellular green alga Volvox carteri following its insertion into the nitrate reductase (nitA) locus. This element, which we have named Jordan, has short (12-bp) terminal inverted repeats and creates a 3-bp target site duplication, like some higher plant transposons of the classic type. Contained within the first 200 bp of one end of t...

The purpose of this paper is to fill a gap in Albert's structure theory' of abstract Jordan algebras of any characteristic $2, by proving the following: THEOREM A. Let 21 be a finite-dimensional Jordan algebra over a field (. Assume (1) that 21 has an identity element u and (2) that every element of 21 has the form au + z, where a e (D and z is nilpotent. Then 21 = 4u + A3, where Z is a nil sub...

The frontal aslant tract (FAT) is a recently described major connection between the preSMA and Broca's area, whose functional role remains undefined. In this study we examined a patient presenting a morphological overregularization strategy in a verb generation task during awake surgery. This specific language deficit coincided with brain tumor resection at the level of the left FAT. During the...

Let R be a 2-torsion free σ-prime ring. It is shown here that if U 6⊂ Z(R) is a σ-Lie ideal of R and a, b in R such that aUb = σ(a)Ub = 0, then either a = 0 or b = 0. This result is then applied to study the relationship between the structure of R and certain automorphisms on R. To end this paper, we describe additive maps d : R −→ R such that d(u) = 2ud(u) where u ∈ U, a nonzero σ-square close...

in this paper, we give a characterization of strongly jordan zero-product preserving maps on normed algebras as a generalization of  jordan zero-product preserving maps. in this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly jordan zero-product preserving maps are completely different. also, we prove that the direct p...