Quasipolar Subrings of 3 x 3 Matrix Rings


Gurgun O., HALICIOĞLU S., Harmanci A.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.21, sa.3, ss.133-146, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Konu: 3
  • Basım Tarihi: 2013
  • Doi Numarası: 10.2478/auom-2013-0048
  • Dergi Adı: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Sayfa Sayıları: ss.133-146

Özet

An element a of a ring R is called quasipolar provided that there exists an idempotent p is an element of R such that p is an element of comm(2)(a), a + p is an element of U(R) and ap is an element of R-qnil. A ring R is quasipolar in case every element in R is quasipolar. In this paper, we determine conditions under which subrings of 3 x 3 matrix rings over local rings are quasipolar. Namely, if R is a bleached local ring, then we prove that J(3)(R) is quasipolar if and only if R is uniquely bleached. Furthermore, it is shown that T-n(R) is quasipolar if and only if T-n(R[[x]]) is quasipolar for any positive integer n.