%0 Journal Article
%A Wood, J.
%A Rogers, E.
%A Owens, D.H.
%D 1998
%F soton:250452
%J Mathematics of Control, Signals, and Systems
%P 40-78
%T A formal theory of matrix primeness
%U https://eprints.soton.ac.uk/250452/
%V 11
%X Primeness of nD polynomial matrices is of fundamental importance in multidimensional systems theory. In this paper we define a quantity which describes the "amount of primeness" of a matrix and identify it as the concept of grade in commutative algebra. This enables us to produce a theory which unifies many existing results, such as the Bezout identities and complementation laws, while placing them on a firm algebraic footing. We also present applications to autonomous systems, behavioural minimality of regular systems, and transfer matrix factorization.