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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Coherent rings of finite weak global dimension


Authors: Edgar E. Enochs, Juan Martínez Hernández and Alberto del Valle
Journal: Proc. Amer. Math. Soc. 126 (1998), 1611-1620
MSC (1991): Primary 13C11, 13D05, 16D40, 16E70
MathSciNet review: 1443151
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Abstract: The category of left modules over right coherent rings of finite weak global dimension has several nice features. For example, every left module 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, Martínez). We will exploit these features of this category to study its objects. In particular, we will consider orthogonal complements (relative to the extension functor) of several classes of modules in this category. In the case of a commutative ring we describe an idempotent radical on its category of modules which, when the weak global dimension does not exceed 2, can be used to analyze the structure of the flat envelopes and of the ring itself.


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Additional Information

Edgar E. Enochs
Affiliation: (Edgar E. Enochs) Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
Email: enochs@ms.uky.edu

Juan Martínez Hernández
Email: juan@fcu.um.es

Alberto del Valle
Affiliation: (Juan Martínez Hernández and Alberto del Valle) Departamento de Matemáticas, Universidad de Murcia, 30001 Murcia, Spain
Email: alberto@fcu.um.es

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04191-4
PII: S 0002-9939(98)04191-4
Keywords: Coherent ring, weak global dimension, flat envelope
Received by editor(s): February 1, 1996
Received by editor(s) in revised form: November 19, 1996
Additional Notes: The second and third authors are supported by the DGICYT of Spain (PB93-0515-C02-02) and by the Comunidad Autónoma de la Región de Murcia (PIB94/25).
Dedicated: Dedicated to the memory of Professor Maurice Auslander
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1998 American Mathematical Society