The Intersection Of Two Ideals And The Intersection Of Two Modules In The Ring Of Multivariate Polynomials Over F

In this paper, we give some fundamental definitions and properties of Grobner basis. We deal with the structure of the intersection of two ideals in A= F[x1, x2,…,xn], which denotes the ring of multivariate polynomials over F. By using the method of Grobner basis, we study the structure related to the intersection of two finitely generated modules over Am. The main structure of this paper is as follows.In Chapter 1, we display some fundamental definitions and properties related to Grdbner basis for the ideal of A= F[x1, x2,…,xn] and the submodule of Am.In Chapter 2, we deduce the structure of the intersection of two ideals in the ring A = F[x1, x2,…,xn].In Chapter 3, we deal with the criterion of reduced Grobner basis of the submodule of Am. By using the method of the syzygy module, we generalize the result of the intersection of two ideals in A to Am.