A note on the multiplicity in factor ring
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
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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.