On Abelian Rings

Agayev N., Harmanci A., Halıcıoğlu S.

TURKISH JOURNAL OF MATHEMATICS, cilt.34, sa.4, ss.465-474, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 4
  • Basım Tarihi: 2010
  • Doi Numarası: 10.3906/mat-0711-1
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.465-474
  • Anahtar Kelimeler: alpha-reduced rings, alpha-symmetric rings, alpha-semicommutative rings, alpha-Armendariz rings, alpha-abelian rings, ARMENDARIZ RINGS, EXTENSIONS, BAER
  • Ankara Üniversitesi Adresli: Evet

Özet

Let alpha be an endomorphism of an arbitrary ring R with identity In this note, we introduce the notion of alpha-abelian rings which generalizes abelian rings We prove that alpha-reduced rings, alpha-symmetric rings, alpha-semicommutative rings and alpha-Armendariz rings are alpha-abelian For a right principally projective ring R, we also prove that R is alpha-reduced if and only if R is alpha-symmetric if and only if R is alpha-semicommutative if and only if R is alpha-Armendariz if and only if R is alpha-Armendariz of power series type if and only if R is alpha-abelian