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A note on form rings and ideals

Published online by Cambridge University Press:  26 February 2010

D. Rees
D. Rees
Affiliation:
Downing College, Cambridge.
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Extract

Let Q be a local ring and let q be an m-primary ideal of Q, where m is the maximal ideal of Q. With q we may associate a ring F(Q, q), termed the form ring of Q relative to the ideal q. If u1, …, um is a basis of q, and if B denotes the quotient ring Q/q, there is a homomorphism of the ring B[X1, …, Xm] of polynomials over B in indeterminates X1 …, Xm onto F(Q, q). The kernel of this homomorphism is a homogeneous ideal of B[X1 …, Xm]. Finally, if a is an ideal of Q there is a homomorphism of F(Q, q) onto F(Q/a, q+a/a). The kernel of this latter homomorphism will be termed the form ideal relative to q of a and denoted by ā.

Type
Research Article
Information
Mathematika , Volume 4 , Issue 1 , June 1957 , pp. 51 - 60
Copyright
Copyright © University College London 1957

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References

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