Bjork's problem about filtered rings and graded rings  

作　　者：周梦 

机构地区：[1]Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

出　　处：《Chinese Science Bulletin》1996年第19期1585-1588,共4页

摘　　要：Let R be a filtered Noetherian ring with identity and M an R-filtered module. The associated graded ring of R is denoted by G(R) and the associated graded G(R) module of M is denoted by gr(M). Bjork studied in ref. [1] the relation between M being a module with a good filtration and gr(M) being a finitely generated module. If R is a ring with positive filtration and G(R) is a Noetherian ring, then M is a module with good filtration if and only if gr(M) is a finitely generated G(R) module. But when R is a Zariski filtered ring,we do not know if the conclusion is true. To be specific, Bjork’s problem is:

关 键 词：filtered RING GRADED RING MODULE with good FILTRATION finitely generated MODULE COMPLETION of filtered module. 

分 类 号：O153.3[理学—数学]