Pure Goldie Dimensions for Exactly Definable Categories

BERKTAŞ M. K.

Bulletin of the Iranian Mathematical Society, cilt.48, sa.1, ss.187-192, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s41980-020-00508-0
  • Dergi Adı: Bulletin of the Iranian Mathematical Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.187-192
  • Anahtar Kelimeler: Pure copresented object, Pure Goldie dimension, Pure injective envelope
  • Uşak Üniversitesi Adresli: Evet

Özet

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.