2004/04/13 by Kiriko Kato, Kato, Kiriko
Mathematics · #13D02 #13D25 #16D90 #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #math.CT #msc:13D02 #msc:13D25 #msc:16D90
paper · pdf · doi:10.48550/arxiv.math/0404243
22 pages
arxiv created 2004/04/13 · openalex publication_date 2004/04/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.