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Journal of the London Mathematical Society Advance Access published online on February 21, 2008
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm124
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© 2008 London Mathematical Society

Stability of Gorenstein categories

Sean Sather-Wagstaff

Department of Mathematical Sciences
Kent State University
Mathematics and Computer Science Building
Summit Street
Kent OH 44242
USA
Current address:
Department of Mathematics
300 Minard Hall
North Dakota State University
Fargo, ND 58105-5075
USA
http://math.ndsu.nodak.edu/faculty/ssatherw/

Tirdad Sharif

School of Mathematics
Institute for Studies in Theoretical Physics and Mathematics
PO Box 19395-5746
Tehran
Iran
sharif@ipm.ir
http://www.ipm.ac.ir/IPM/people/personalinfo.jsp?PeopleCode=IP0400060

Diana White

Department of Mathematics
University of Nebraska
203 Avery Hall
Lincoln, NE 68588-0130
USA
Current address:
Department of Mathematics
LeConte College
1523 Greene Street
University of South Carolina
Columbia, SC 29208
USA
dwhite@math.sc.edu
http://www.math.sc.edu~dwhite/

We show that an iteration of the procedure used to define the Gorenstein projective modules over a commutative ring R yields exactly the Gorenstein projective modules. Specifically, given an exact sequence of Gorenstein projective R-modules


Formula

such that the complexes HomR(G, H) and HomR(H, G) are exact for each Gorenstein projective R-module H, the module Coker(Formula ) is Gorenstein projective. The proof of this result hinges upon our analysis of Gorenstein subcategories of abelian categories.

2000 Mathematics Subject Classification 13C05, 13D02, 13D07, 18G10, 18G15.

Tirdad Sharif is supported by a grant from IPM\ (No. 83130311).

Received March 21, 2007;
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