WebMar 26, 2009 · For any ring R and any positive integer n we prove that a left R-module is a Gorenstein n-syzygy if and only if it is an n-syzygy Over a left and right Noetherian ring we introduce the... WebDec 23, 2015 · This especially extends a recent result of Araya and Iima concerning a Cohen–Macaulay local ring with canonical module to an arbitrary local ring. ... Commutative Non-Noetherian Rings with the Diamond Property. 17 May 2024. Miodrag C. Iovanov. ... Reiten, I: Syzygy modules for Noetherian rings. J Algebra 183 (1), 167–185 (1996)
CiteSeerX — Syzygy modules for quasi k-Gorenstein rings
WebFeb 14, 2024 · 99 Accesses 4 Citations Metrics Abstract Let R be a commutative Noetherian ring. We consider the question of when n -syzygy modules over R are n -torsionfree in the sense of Auslander and Bridger. Our tools include Serre’s condition and certain conditions on the local Gorenstein property of R. WebFeb 21, 2005 · Syzygy modules with semidualizing or G-projective summands February 2005 Authors: Ryo Takahashi Abstract Let R be a commutative Noetherian local ring with residue class field k. In this... blust international cincinnati
A CODIMENSION THEOREM FOR PSEUDO-NOETHERIAN RINGS
Websyzygy: 1 n the straight line configuration of 3 celestial bodies (as the sun and earth and moon) in a gravitational system Type of: physical phenomenon a natural phenomenon … WebIn mathematics, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; if the chain condition is satisfied only for left ideals or for right ideals, then the ring is said left-Noetherian or right-Noetherian respectively. That is, every increasing sequence of left (or right) ideals has a largest element; that is, there exists an n … WebLet R be a commutative noetherian ring. Let n ≥ 0 be an integer. Then the following three conditions are equivalent. The ring R satisfies (Gn−1) and (Sn). For an R-module M one has: M is n-syzygy M is n-torsionfree M satisfies (Sn). For an R-module M one has: M is (n +1)-syzygy M is (n+ 1)-% torsionfree. blust international