Pure Goldie Dimensions for Exactly Definable Categories

BERKTAŞ M. K.

Bulletin of the Iranian Mathematical Society, vol.48, no.1, pp.187-192, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1007/s41980-020-00508-0
  • Journal Name: Bulletin of the Iranian Mathematical Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.187-192
  • Keywords: Pure copresented object, Pure Goldie dimension, Pure injective envelope
  • Uşak University Affiliated: Yes

Abstract

It is shown that if A is an object in an exactly definable category C such that A has finite pure Goldie dimension and that every pure monomorphism A→ A is an isomorphism, then its endomorphism ring End C(A) is semilocal. Also, it is proved that every subobject of a pure quotient finite dimensional pure injective object of an exactly definable category has a semilocal endomorphism ring.