SOME REMARKS ON CATEGORIES OF MODULES MODULO MORPHISMS WITH ESSENTIAL KERNEL OR SUPERFLUOUS IMAGE

- Journal title : Journal of the Korean Mathematical Society
- Volume 50, Issue 3, 2013, pp.557-578
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2013.50.3.557

Title & Authors

SOME REMARKS ON CATEGORIES OF MODULES MODULO MORPHISMS WITH ESSENTIAL KERNEL OR SUPERFLUOUS IMAGE

Alahmadi, Adel; Facchini, Alberto;

Alahmadi, Adel; Facchini, Alberto;

Abstract

For an ideal of a preadditive category , we study when the canonical functor is local. We prove that there exists a largest full subcategory of , for which the canonical functor is local. Under this condition, the functor , turns out to be a weak equivalence between , and . If is additive (with splitting idempotents), then is additive (with splitting idempotents). The category is ample in several cases, such as the case when =Mod-R and is the ideal of all morphisms with essential kernel. In this case, the category contains, for instance, the full subcategory of Mod-R whose objects are all the continuous modules. The advantage in passing from the category to the category lies in the fact that, although the two categories and are weakly equivalent, every endomorphism has a kernel and a cokernel in , which is not true in . In the final section, we extend our theory from the case of one ideal to the case of ideals , , .

Keywords

preadditive category;additive functor;local functor;essential kernel;superfluous image;

Language

English

Cited by

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