Feckly reduced rings

ÜNGÖR B., Gurgun O., HALICIOĞLU S., Harmanci A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.44, sa.2, ss.375-384, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.15672/hjms.2015449413
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.375-384
  • Anahtar Kelimeler: reduced ring, feckly reduced ring, EXCHANGE RINGS, REGULAR RINGS, ELEMENTS
  • Ankara Üniversitesi Adresli: Evet

Özet

Let R be a ring with identity and J(R) denote the Jacobson radical of R. In this paper, we introduce a new class of rings called feckly reduced rings. The ring R is called feckly reduced if R/J(R) is a reduced ring. We investigate relations between feckly reduced rings and other classes of rings. We obtain some characterizations of being a feckly reduced ring. It is proved that a ring R is feckly reduced if and only if every cyclic projective R-module has a feckly reduced endomorphism ring. Among others we show that every left Artinian ring is feckly reduced if and only if it is 2-primal, R is feckly reduced if and only if T(R, R) is feckly reduced if and only if R[x]/ < x(2) > is feckly reduced.