2012/11/25 by Moharram Aghapournahr, Aghapournahr, Moharram, Kamal Bahmanpour +1
Computer Science · Mathematics · Medicine · #13D45 #13E05 #14B15 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Intracranial Aneurysms: Treatment and Complications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1211.5748
openalex publication_date 2012/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let I be an ideal of a Noetherian ring R and M be a finitely generated R-module. We introduce the class of extension modules of finitely generated modules by the class of all modules T with dim T≤ n and we show it by \rm FD≤ n where n≥ -1 is an integer. We prove that for any \rm FD≤ 0(or minimax) submodule N of HtI(M) the R-modules \rm HomR(R/I,HtI(M)/N) \rm and \rm Ext1R(R/I,HtI(M)/N) are finitely generated, whenever the modules H0I(M), H1I(M), ..., Ht-1I(M) are \rm FD≤ 1 (or weakly Laskerian). As a consequence, it follows that the associated primes of HtI(M)/N are finite. This generalizes the main results of Bahmanpour and Naghipour, Brodmann and Lashgari, Khashyarmanesh and Salarian, and Hong Quy. We also show that the category \mathscr FD1(R,I)cof of I-cofinite \rm FD≤1 ~ R-modules forms an Abelian subcategory of the category of all R-modules.