International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 8, Pages 439-451
doi:10.1155/S0161171202011675
On ideals and homology in additive categories
Department of Mathematics, Illinois State University, Normal 61790-4520, IL, USA
Received 28 January 2001; Revised 26 July 2001
Copyright © 2002 Lucian M. Ionescu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Ideals are used to define homological functors in additive
categories. In abelian categories the ideals corresponding to the
usual universal objects are principal, and the construction
reduces, in a choice dependent way, to homology groups.
The applications considered in this paper are: derived
categories and functors.