English

Morphisms represented by monomorphisms

Commutative Algebra 2007-05-23 v1 Category Theory

Abstract

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.

Keywords

Cite

@article{arxiv.math/0404243,
  title  = {Morphisms represented by monomorphisms},
  author = {Kiriko Kato},
  journal= {arXiv preprint arXiv:math/0404243},
  year   = {2007}
}

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22 pages