(D-4)-Objects in Abelian Categories

KALEBOĞAZ B., KESKİN TÜTÜNCÜ D.

ALGEBRA COLLOQUIUM, vol.29, no.02, pp.231-240, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 02
  • Publication Date: 2022
  • Doi Number: 10.1142/s1005386722000190
  • Journal Name: ALGEBRA COLLOQUIUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.231-240
  • Keywords: (D-4)-object, abelian category
  • Hacettepe University Affiliated: Yes

Abstract

Let A be an abelian category and M is an element of A. Then M is called a (D-4)-object if, whenever A and B are subobjects of M with M = A circle plus B and f : A -> B is an epimorphism, Ker f is a direct summand of A. In this paper we give several equivalent conditions of (D-4)-objects in an abelian category. Among other results, we prove that any object M in an abelian category A is (D-4) if and only if for every subobject K of M such that K is the intersection K-1 boolean AND K-2 of perspective direct summands K-1 and K-2 of M with M = K-1 + K-2, every morphism phi: M -> M/K can be lifted to an endomorphism theta: M -> M in End(A)(M).