Rings in which elements are a sum of a central and a unit element

KURTULMAZ Y., HALICIOĞLU S., Harmanci A., Chen H.

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, cilt.26, sa.4, ss.619-631, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 4
  • Basım Tarihi: 2019
  • Dergi Adı: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.619-631
  • Anahtar Kelimeler: CU ring, CU-decomposition, matrix ring, uniquely nil clean ring, *-clean ring, nil *-clean ring
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper we introduce a new class of rings whose elements are a sum of a central and a unit element, namely a ring R is called CU if each element a is an element of R has a decomposition a = c + u where c is central and u is unit. One of the main results in this paper is that if F is a field which is not isomorphic to Z(2), then M-2(F) is a CU ring. This implies, in particular, that any square matrix over a field which is not isomorphic to Z(2) is the sum of a central matrix and a unit matrix.