On feckly clean rings

Chen H., KÖSE H., Kurtulmaz Y.

Journal of Algebra and its Applications, cilt.14, sa.4, 2015 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 4
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1142/s0219498815500462
  • Dergi Adı: Journal of Algebra and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Feckly clean ring, pm-ring, strongly zero dimensional space
  • Ankara Üniversitesi Adresli: Evet

Özet

A ring R is feckly clean provided that for any a R there exists an element e R and a full element u R such that a = e + u, eR(1 - e) J(R). We prove that a ring R is feckly clean if and only if for any a R, there exists an element e R such that V(a) V(e), V(1 - a) V(1 - e) and eR(1 - e) J(R), if and only if for any distinct maximal ideals M and N, there exists an element e R such that e M, 1 - e N and eR(1 - e) J(R), if and only if J-spec(R) is strongly zero-dimensional, if and only if Max(R) is strongly zero-dimensional and every prime ideal containing J(R) is contained in a unique maximal ideal. More explicit characterizations are also discussed for commutative feckly clean rings.