Nil-quasipolar rings

Gurgun O., HALICIOĞLU S., Harmanci A.

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, cilt.20, sa.1, ss.29-38, 2014 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 1
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s40590-014-0005-y
  • Dergi Adı: BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.29-38
  • Hacettepe Üniversitesi Adresli: Evet

Özet

Let R be an arbitrary ring. An element a is an element of R is nil-quasipolar if there exists p(2) = p is an element of comm(2)(a) such that a + p is an element of Nil(R); R is called nil-quasipolar in case each of its elements is nil-quasipolar. In this paper, we study nil-quasipolar rings over commutative local rings. We determine the conditions under which a single 2x2 matrix over a commutative local ring is nil-quasipolar. It is shown that A is an element of M-2(R) is nil-quasipolar if and only if A is an element of Nil(M-2(R)) or A + I-2 is an element of Nil (M-2(R)) or the characteristic polynomial chi(A) has a root in Nil(R) and a root in -1 + Nil(R). Wegive some equivalent characterizations of nil-quasipolar rings through the endomorphism ring of a module. Among others we prove that every nil-quasipolar ring has stable range one.