COHERENT RINGS OF FINITE WEAK GLOBAL DIMENSION

Citation
Ee. Enochs et al., COHERENT RINGS OF FINITE WEAK GLOBAL DIMENSION, Proceedings of the American Mathematical Society, 126(6), 1998, pp. 1611-1620
Citations number
14
Categorie Soggetti
Mathematics,Mathematics,Mathematics,Mathematics
ISSN journal
00029939
Volume
126
Issue
6
Year of publication
1998
Pages
1611 - 1620
Database
ISI
SICI code
0002-9939(1998)126:6<1611:CROFWG>2.0.ZU;2-E
Abstract
The category of left modules over right coherent rings of finite weak global dimension has several nice features. For example, every left mo dule over such a ring has a flat cover (Belshoff, Enochs, Xu) and, if the weak global dimension is at most two, every left module has a flat envelope (Asensio, Martinez). We will exploit these features of this category to study its objects. In particular, we will consider orthogo nal complements (relative to the extension functor) of several classes of modules in this category. In the case of a commutative ring we des cribe an idempotent radical on its category of modules which, when the weak global dimension does not exceed 2, can be used to analyze the s tructure of the flat envelopes and of the ring itself.