Pure Goldie Dimensions for Exactly Definable Categories
Bulletin of the Iranian Mathematical Society, cilt.48, sa.1, ss.187-192, 2022 (SCI-Expanded, Scopus)
- 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.