arXiv subjects
Publications and source records attributed to I. Paniello.
We extend the classical associative PI-theory to Associative Pairs, and in doing so, we introduce related notions already present for algebras (and Jordan systems) as the ones of PI-element and PI-ideal, extended centroid and central closure.
We consider the set of ($n\times n\times n$) cubic stochastic matrices of type (1,2) together with different multiplication rules that not only retain their stochastic properties but also endow this set with an associative semigroup structure. Then we introduce different actions of the semigroup of nonnegative column stochastic $n\times n$ matrices on the set of cubic stochastic matrices of type (1,2) and study how these actions translate to the cubic matrix slices and marginal distributions. Actions introduced here provide an algebraic framework where considering different changes affecting the transition probabilities ruling certain biological populations.
We study a notion of order in Jordan algebras based on the version for Jordan algebras of the ideas of Fountain and Gould as adapted to the Jordan context by Fernández-López and Garc\'ıa-Rus, making use of results on general algebras of quotients of Jordan algebras. In particular, we characterize the set of Lesieur-Croisot elements of a nondegenerate Jordan algebra as those elements of the Jordan algebra lying in the socle of its maximal algebra of quotients, and apply this relationship to extend to quadratic Jordan algebras the results of Fernández-López and Garc\'ıa-Rus on local orders in nondegenerate Jordan algebras satisfying the descending chain condition on principal inner ideals and not containing ideals which are nonartinian quadratic factors.