The Algebras Mn , n ( E ) and Mn ( E ) ⊗ E in Positive Characteristic

In characteristic zero the algebras Mn(E)⊗E andMn,n(E) appear in the list of non-trivial verbally-prime algebras. Verbally-prime algebras play a proeminent role in Kemer’s results about structure of the varieties of associative algebras in characteristic zero (see [8] for a detailed account of it). Recently, some new results have been obtained about the behavior of polynomial identities satisfied by the verbally-prime algebras, giving a new proof that the so called Kemer’s Tensor Product Theorem is no longer valid in positive characteristic (see [1], [2], [3], [4], [5], [6] and [7] for a detailed account of this research).