ABSTRACT
Chapter 17 Wakamatsu Tilting Modules, U-Dominant Dimension, and k-Gorenstein Modules Zhaoyong Huang Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China huangzy@nju.edu.cn
17.1 Introduction and Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 17.2 Wakamatsu Tilting Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 17.3 The Proof of Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 17.4 Exactness of the Double Dual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 17.5 A Generalization of k-Gorenstein Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Abstract Let and be left and right noetherian rings and U a Wakamatsu tilting module with = End(T ). We introduce a new definition of U -dominant dimensions and show that the U -dominant dimensions of U and U are identical. We characterize k-Gorenstein modules in terms of homological dimensions and the property of double homological functors preserving monomorphisms. We also study a generalization of k-Gorenstein modules, and characterize it in terms of some similar properties of k-Gorenstein modules. Subject classifications: 16E10, 16E30, 16D90. Keywords: U -dominant dimension, k-Gorenstein modules, Wakamatsu tilting modules, flat dimension.
