학술논문
Rees algebra over an ideal in $\germ{t}$-rings.
Document Type
Journal
Author
Singh, Jyoti (6-MNNIT) AMS Author Profile; Kumar, Shiv Datt (6-MNNIT) AMS Author Profile
Source
Subject
13 Commutative algebra -- 13A General commutative ring theory
13A30Associated graded rings of ideals
13Commutative algebra -- 13E Chain conditions, finiteness conditions
13E05Noetherian rings and modules
13A30
13
13E05
Language
English
Abstract
Summary: ``If there exists a finitely generated module $M$ over a $\germ t$-ring such that $\germ tM=Ann_M\germ t$ and $M/\germ tM$ is of finite length, then we show that commutator ideal $[q,q]$ is contained in $\germ tq$, for some prime ideal $q$ under certain conditions. Using this property, we discuss the Noetherian property of the Rees algebra of the prime ideal $q$ in $\germ t$-ring and as an application we give an analogue of the Artin-Rees lemma for $\germ t$-rings.''