DECOMPOSITIONS OF 2 x 2 MATRICES OVER LOCAL RINGS

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Chen H., HALICIOĞLU S., KÖSE H.

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, cilt.100, sa.114, ss.287-298, 2016 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 100 Sayı: 114
  • Basım Tarihi: 2016
  • Doi Numarası: 10.2298/pim1614287c
  • Dergi Adı: PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.287-298
  • Anahtar Kelimeler: perfectly clean ring, perfectly J-clean ring, quasipolar ring, matrix, triangular matrix, STRONGLY CLEAN MATRIX, QUASIPOLAR RINGS
  • Ankara Üniversitesi Adresli: Evet

Özet

An element a of a ring R is called perfectly clean if there exists an idempotent e is an element of comm(2) (a) such that a - e is an element of U(R). A ring R is perfectly clean in case every element in R is perfectly clean. In this paper, we completely determine when every 2 x 2 matrix and triangular matrix over local rings are perfectly clean. These give more explicit characterizations of strongly clean matrices over local rings. We also obtain several criteria for a triangular matrix to be perfectly J-clean. For instance, it is proved that for a commutative local ring R, every triangular matrix is perfectly J-clean in T-n (R) if and only if R is strongly J-clean.