Relative Homological Algebra
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Author(s): E. E. Enochs and O. M. G. Jenda
Publisher: Walter de Gruyter
ISBN:  3 1101 6633 X
Format: hardback
  339pp
Price: DM168
Review Date: May 23, 2000
Review: Since the introduction of relative homological algebra in 1965, more theorems have been found to guarantee the existence of precovers, covers, preenvelopes and envelopes. These are the basic objects of the subject and are used to construct resolutions and then left and right derived functions. Other useful items that have come into play are various versions of Wakamatsu lemma, the notions of special precovers and preenvelopes and the orthogonality of classes of objects of an abelian category with respect to the extension functor. This book gives a systematic treatment of this subject, along with its new developments and applications. There are twelve chapters. the first three, made up from the authors' lecture notes, are suitable for an introductory course in module and ring theory and give the basic tools and notation. Other chapters discuss: torsion free covering modules; covers; envelopes; covers, envelopes and cotorsion theories; relative homological algebras and balance; Iwanaga-Gorenstein and Coker-Macauley rings and their modules; Gorenstein modules; Gorenstein covers and envelopes; and balance over Gorenstein and Cohen-Macauley rings.