B-sequence and approximations of generalized Cohen-Macaulay ideals

2003/07/17 by Yukihide Takayama, Takayama, Yukihide
Mathematics · #13C99 #13D45 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13C99 #msc:13D45

paper · pdf · doi:10.48550/arxiv.math/0307232

This is a largely enhanced version of "Single spot ideals of codimension 3 and long Bourbaki sequences"(math.AC/0303384)

arxiv created 2003/07/17 · openalex publication_date 2003/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of b-sequence for finitely generated modules over Noetherian rings, which characterizes long Bourbaki sequences. Our main concern is an application of this notion to generalized Cohen-Macaulay approximation, which we introduced lately. We will show how we can construct long Bourbaki sequences of non-trivial type characterizing generalized Cohen-Macaualy ideals by finding suitable b-sequences.

Related

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