A GENERALIZATION OF REFLEXIVE RINGS

Calci M. B., Chen H., HALICIOĞLU S.

MATHEMATICA BOHEMICA, 2023 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2023
  • Doi Numarası: 10.21136/mb.2023.0034-221
  • Dergi Adı: MATHEMATICA BOHEMICA
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: reflexive ring, reversible ring, J-reflexive ring, J-reversible ring, ring extension
  • Ankara Üniversitesi Adresli: Evet

Özet

We introduce a class of rings which is a generalization of reflexive rings and J-reversible rings. Let R be a ring with identity and J(R) denote the Jacobson radical of R. A ring R is called J-reflexive if for any a, b is an element of R, aRb = 0 implies bRa subset of J(R). We give some characterizations of a J-reflexive ring. We prove that some results of reflexive rings can be extended to J-reflexive rings for this general setting. We conclude some relations between J-reflexive rings and some related rings. We investigate some extensions of a ring which satisfies the J-reflexive property and we show that the J-reflexive property is Morita invariant.