Regular morphisms in abelian categories


Crivei S., Kosan M. T. , Yildirim T.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.18, sa.9, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Konu: 9
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1142/s0219498819501809
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Özet

We establish some properties involving regular morphisms in abelian categories. We show a decomposition theorem on the image of a regular sum of morphisms, a characterization of regular morphisms in terms of consecutive pairs of morphisms, and a description of certain equivalent morphisms. We also generalize Ehrlich's Theorem on one-sided unit regular morphisms by showing that if N is an M-regular object, then a morphism f : M -> N is left (right) unit regular if and only if there exists a split monomorphism (epimorphism) Ker(f) -> Coker(f). We also study regular morphisms determined by generalized inverses in additive categories.