2015/05/06 by A. V. Jayanthan, Jayanthan, A. V., B. Ramachandran +2
Mathematics · Medicine · #13A30 #13D40 #Algebraic structures and combinatorial models #Cholinesterase and Neurodegenerative Diseases #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13A30 #msc:13D40
paper · pdf · doi:10.48550/arxiv.1505.01251
16 pages
arxiv created 2015/05/06 · openalex publication_date 2015/05/06 · arxiv updated 2015/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1960, D.G. Northcott proved that if e0(I) and e1(I) denote zeroth and first Hilbert-Samuel coefficients of an \mathfrak m-primary ideal I in a Cohen-Macaulay local ring (R,\mathfrak m), then e0(I)-e1(I)≤ ℓ (R/I). In this article, we study an analogue of this inequality for Buchsbaum-Rim coefficients. We prove that if (R,\mathfrak m) is a two dimensional Cohen-Macaulay local ring and M is a finitely generated R-module contained in a free module F with finite co-length, then br0(M)-br1(M)≤ ℓ (F/M), where br0(M) and br1(M) denote zeroth and first Buchsbaum-Rim coefficients respectively.