COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics


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Colloquium: Symmetric Algebras and Grbner Bases


4:10 p.m. Neill Hall 5W

Zhongming Tang

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. Grbner bases will play an important role in our discussion.