Abstract
For any ideal Q in any local ring R such that Q is primary for M(R),by e(Q) we denote the multiplicity of Q; also by e(R) we denote the multiplicity of R,i.e., (R) = e(M(R)); for definition see [28: page 294]; from the definition it follows that e(QR*) _ e(Q) ≥ e(R) = e(R*) where R* is the completion of R; note that by [28: Theorem 23 on page 296] we know that if R is regular then e(R) = 1.
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© 1998 Springer-Verlag Berlin Heidelberg
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Abhyankar, S.S. (1998). Some Cases of Three-Dimensional Birational Resolution. In: Resolution of Singularities of Embedded Algebraic Surfaces. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03580-1_4
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DOI: https://doi.org/10.1007/978-3-662-03580-1_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08351-8
Online ISBN: 978-3-662-03580-1
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