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SPECIAL PRECOVERS IN COTORSION THEORIES

Published online by Cambridge University Press:  17 June 2002

Karen D. Akinci  and
Rafail Alizade
Karen D. Akinci
Affiliation:
Izmir University of Economics, Balcova Campus, Izmir, Turkey (karen.akinci@izmirekonomi.edu.tr)
Rafail Alizade
Affiliation:
Department of Mathematics, Izmir Technology Institute, Gülbahçeköyü, Urla, Izmir, Turkey (alizade@likya.iyte.edu.tr)
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Abstract

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A cotorsion theory is defined as a pair of classes Ext-orthogonal to each other. We give a hereditary condition (HC) which is satisfied by the (flat, cotorsion) cotorsion theory and give properties satisfied by arbitrary cotorsion theories with an HC. Given a cotorsion theory with an HC, we consider the class of all modules having a special precover with respect to the first class in the cotorsion theory and show that this class is closed under extensions. We then raise the question of whether this class is resolving or coresolving.

AMS 2000 Mathematics subject classification: Primary 18G15. Secondary 18E40

Keywords

cotorsion theoryhereditary conditionspecial precoverspecial pre-envelope
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 2 , June 2002 , pp. 411 - 420
Copyright
Copyright © Edinburgh Mathematical Society 2002