On Frobenius full matrix algebras with structure systems

Abstract

Let n ≥ 2 be an integer. In [5] and [6], an n × n A-full matrix algebra over a field K is defined to be the set Mn(K) of all square n × n matrices with coefficients in K equipped with a multiplication defined by a structure system A, that is, an n-tuple of n × n matrices with certain properties. In [5] and [6], mainly A-full matrix algebras having (0, 1)-structure systems are studied, that is, the structure systems A such that all entries are 0 or 1. In the present paper we study A-full matrix algebras having non (0, 1)-structure systems. In particular, we study the Frobenius Afull matrix algebras. Several infinite families of such algebras with nice properties are constructed in Section 4.