Solving bose conjecture on linear multidimensional systems

摘要

The conjecture proposed by J.P. Serre in 1955 saying that a projective module over a polynomial ring is free has been solved independently in 1976 by D. Quillen and A.A. Suslin. As a generalization of it, N.K. Bose and Z. Lin proposed in 1998 a conjecture on the possibility to factorize a certain type of full rank polynomial matrices through zero prime polynomial matrices in order to factor out the P.G.C.D. of the major minors. Our purpose is to use the powerful methods of algebraic analysis pioneered by V.P. Palamodov and M. Kashiwara in 1970 in order to solve positively this conjecture while giving its module theoretic meaning.