A Normal Form Algorithm for Modules overk[x, y]/left angle bracketxyright-pointing angle bracket Original Research Article

This paper gives an algorithm to classify finitely generated modules over the ringk[x, y]/left angle bracketxyright-pointing angle bracket,kany field. The given module is presented as the cokernel of a matrix with entries in the ring. Our algorithm reduces this matrix to a normal form analogous to the Smith normal form for a matrix over a polynomial ring in one variable. A natural application is the classification of pairs of mutually annihilating linear operators on a vector space.