Colloquium: Symmetric Algebras and Gröbner Bases
4:10 p.m. Neill Hall 5W
Abstract Let R be a commutative Noetherian ring and M a finitely generated R-module. Then the symmetric algebra, Sym(M), of M has the form Sym(M) = R[X1, …, Xn]/J. Let < be a monomial order on the monomials in X1, …, Xn and in(J) the initial ideal of J. One can obtain some properties of Sym(M) from that of R[X1, …, Xn]/in(J), which is relatively simple since in(J) is a monomial ideal. We will introduce s-sequences. Gröbner bases will play an important role in our discussion.