The Amitsur-Levitzki theorem asserts that Mn(F ) satisfies a polynomial identity of degree 2n. (Here, F is a field and Mn(F ) is the algebra of n × n matrices over F ). It is easy to give examples of subalgebras of Mn(F ) that do satisfy an identity of lower degree and subalgebras of Mn(F ) that satisfy no polynomial identity of degree ≤ 2n − 2. In this paper we prove that the subalgebras of n ...

In this paper, we prove various results concerning DGA-algebras in the context of the Homological Perturbation Theory. We distinguish two class of contractions for algebras: full algebra contractions and semi-full algebra contractions. A full algebra contraction is, in particular , a semi-full algebra contraction. Taking a full algebra contraction and an \algebra perturbation" as data of the Ba...

We propose in this paper a distributed packed storage format that exploits the symmetry or the triangular structure of a dense matrix. This format stores only half of the matrix while maintaining most of the efficiency compared to a full storage for a wide range of operations. This work has been motivated by the fact that, contrary to sequential linear algebra libraries (e.g. LAPACK [4]), there...