On Exchange Rings

Özdin T., Dumlu Polat H.

2nd International E-Conference on Mathematical and Statistical Science: A Selcuk Meeting, Konya, Türkiye, 5 - 07 Haziran 2023, ss.184

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Konya
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.184
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

Exchange ring have been characterized by the property that for all a ∈ R, there exist an idempotent e ∈ aR such that (1 − e) ∈ (1 − a)R. A unit-picker is a map G that associates to every ring R a well-defined set G(R) of central units in R such that G(R) is invariant under isomorphism of rings. In [5] An element q in a ring R is called a G-idempotent (or quasi-idempotent [4]) if q 2 = gq for some g ∈ G or, equivalently, g −1 q is an idempotent for some g ∈ G. In this work we introduce the notation of G-exchange ring via G-idempotent and give some relation betweenG-exchange ring and (strongly)-G clean ring.