Rings in which Every Element is a Sum of Two Tripotents

Ying Z., Kosan T., Zhou Y.

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, cilt.59, sa.3, ss.661-672, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 3
  • Basım Tarihi: 2016
  • Doi Numarası: 10.4153/cmb-2016-009-0
  • Dergi Adı: CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.661-672
  • Anahtar Kelimeler: idempotent, tripotent, Boolean ring, polynomial identity x(3) = x, polynomial identity x(6) = x(4), polynomial identity x(8) = x(4), NIL-CLEAN RINGS
  • Gazi Üniversitesi Adresli: Hayır

Özet

Let R be a ring. The following results are proved. (1) Every element of R is a sum of an idempotent and a tripotent that commute if and only if R has the identity x(6) = x(4) if and only if R congruent to R-1 x R-2, where R-1/J(R-1) is Boolean with U(R-1) a group of exponent 2 and R-2 is zero or a subdirect product of Z(3)'s. (2) Every element of R is either a sum or a difference of two commuting idempotents if and only if R congruent to R-1 x R-2, where R-1/J(R-1) is Boolean with J(R-1) = 0 or J(R-1) = {0, 2} and R-2 is zero or a subdirect product of Z(3)'s. (3) Every element of R is a sum of two commuting tripotents if and only if R congruent to R-1 x R-2 x R-3, where R-1/J(R-1) is Boolean with U(R-1) a group of exponent 2, R-2 is zero or a subdirect product of Z(3)'s, and R-3 is zero or a subdirect product of Z(5)'s.