International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 8, Pages 439-451

On ideals and homology in additive categories

Lucian M. Ionescu

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.


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.