A note on the multiplicity in factor ring

Mathematica Slovaca - Tập 58 - Trang 173-176 - 2008
Eduard Boďa1
1Department of Algebra, Geometry and Didactic of Mathematics, Faculty of Mathematics Physics and Informatics Comenius University, Bratislava, Slovakia

Tóm tắt

Let (R,m) = k[x 1,..., x n ](x 1,...,x n ) be a local polynomial ring (k being an algebraically closed field), and Q:= (F 1,..., F r )R be a primary ideal in R with respect to a maximal ideal m ⊂ R. In this short note we give a formula for the multiplicity e 0 (QR/(F 1)R, R/(F 1)R).

Tài liệu tham khảo

Boďa, E. —Farnbauer, R.: On the standard basis and multiplicity of (Xa — Y b, Xc — Y d), Acta Math. Univ. Comenian. (N.S.) 72 (2003), 15–22. Matsumura, H.: Commutative Ring Theory. Cambridge Stud. Adv. Math. 8, Cambridge Univ. Press, Cambridge, 1986. Northcott, D. G.: Lessons on Rings, Modules and Multiplicities, Cambridge Univ. Press, Cambridge, 1968. Zariski, O. —Samuel, P.: Commutative Algebra, D. Van Nostrand company, Toronto-London-New York, 1958.