3-standardness of the maximal ideal

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• 作者：H. Ananthnarayan^a ; ^{ahariharan2@math.unl.edu"" rel=""nofollow} ; Craig Huneke^b ; ^{huneke@math.ku.edu"" rel=""nofollow}
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2011
• 出版时间：November 2011
• 年：2011
• 卷：215
• 期：11
• 页码：2674-2683
• 全文大小：265 K

文摘

We study a notion called n-standardness (defined by M.E. Rossi (2000) in [10] and extended in this paper) of ideals primary to the maximal ideal in a Cohen–Macaulay local ring and some of its consequences. We further study conditions under which the maximal ideal is 3-standard, first proving results for when the residue field has prime characteristic and then using the method of reduction to prime characteristic to extend the results to the equicharacteristic 0 case. As an application, we extend a result due to T. Puthenpurakal (2005) [9] and show that a certain length associated with a minimal reduction of the maximal ideal does not depend on the minimal reduction chosen.