Weak invertibility of linear finite automata .2. Reduction from rings to fields

Let H denote the set of all possible transfer function matrices of weakly invertible linear finite automata over a finite commutative ring R with identity. This paper gives a series of natural reductions, reduces the problem of classification and enumeration of H. to the case when R is a finite field. 1991 Mathematics Subject Classification: 68Q70, 15A21, 15A33.