Relative syzygies and grade of modules

Abstract

Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslander and Bridger and the Cohen-Macaulay approximation theorem due to Auslander and Buchweitz. In this paper we generalize these results to much more general case over non-commutative rings. As an application, we establish a relation between the injective dimension of a generalized tilting module ω and the finitistic dimension with respect to ω.

Novel flame-retardant epoxy composites containing aluminium β-carboxylethylmethylphosphinate

“…They are predicted to be the largest growing share of the flame retardant market. The most used phosphorus compounds in EP for EE application include red phosphorus [5], melamine polyphosphate [6], aromatic phosphates such as triphenyl phosphate [7], dihydrooxaphosphaphenantrene, and its derivatives [8,9], as well as metal phosphinates [10][11][12].…”