Functionally recursive rings of matrices-Two examples

摘要

We define the notions of finite-state and functionally recursive matrices andtheir growth. We also introduce two rings generated by functionally recursivematrices. The first is isomorphic to the 2-generated free ring. The second is a2-generated monomial ring such that the multiplicative semigroup of monomialsin the generators is nil of degree 5 and the ring has Gelfand Kirillovdimension 1 + log(2)/log(a) where a=1/2(1+sqrt(5)).