Morphisms represented by monomorphisms
交换代数
2007-05-23 v1 范畴论
摘要
Every homomorphism of modules is projective-stably equivalent to an epimorphism but is not always to a monomorphism. We prove that a map is projective-stably equivalent to a monomorphism if and only if its kernel is torsionless, that is, a first syzygy. If it occurs although, there can be various monomorphisms that are projective-stably equivalent to a given map. But in this case there uniquely exists a "perfect" monomorphism to which a given map is projective-stably equivalent.
引用
@article{arxiv.math/0404243,
title = {Morphisms represented by monomorphisms},
author = {Kiriko Kato},
journal= {arXiv preprint arXiv:math/0404243},
year = {2007}
}
备注
22 pages