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Communications in Algebra Volume 31, 2003 - Issue 11
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Original Articles

The Length of Noetherian Polynomial Rings

Gary Brookfield Department of Mathematics, California State University, Los Angeles, California, USA; Department of Mathematics, California State University, Los Angeles, CA, 90032, USACorrespondence[email protected]
Pages 5591-5607 | Received 01 Jun 2002, Published online: 31 Aug 2006
 
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Abstract

We show that if R is a left Noetherian ring, then

Here, for a Noetherian left module A, len A is its ordinal valued length as defined by Gulliksen (Gulliksen, (1973). T. H. A theory of length for noetherian modules. J. Pure Appl. Algebra 3:159–170), and ⊗ is the natural product on ordinal numbers.

Acknowledgments

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