New Simple Algebras Containing the Matrix Ring

Abstract

We define the combinatorial simple algebras N(eAS,n,t)k, N(eAS,n,t)k+and N(eAS,n,t)[k]which contain both the matrix ring and the non-associative algebras discussed in [11]. We also define a new cyclic finite dimensional algebra which contains the matrix ring Mn(𝔽) and show that the algebra is simple (see [3] and [7]). Even more, we find the automorphism group of the algebra N(0,n,t)[1]and show that the general matrix group GLn+t(𝔽) is not a subgroup of the automorphism group Aut (N(0,n,t)[1]).