Rings with each right ideal automorphism-invariant

Kosan M. T., Truong Cong Quynh T. C. Q., Srivastava A. K.

JOURNAL OF PURE AND APPLIED ALGEBRA, cilt.220, sa.4, ss.1525-1537, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 220 Sayı: 4
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.jpaa.2015.09.016
  • Dergi Adı: JOURNAL OF PURE AND APPLIED ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1525-1537
  • Gazi Üniversitesi Adresli: Hayır

Özet

In this paper, we study rings having the property that every right ideal is automorphism-invariant. Such rings are called right a-rings. It is shown that (1) a right a-ring is a direct sum of a square-full semisimple artinian ring and a right square-free ring, (2) a ring R is semisimple artinian if and only if the matrix ring M-n(R) is a right a-ring for some n > 1, (3) every right a-ring is stably-finite, (4) a right a-ring is von Neumann regular if and only if it is semiprime, and (5) a prime right a-ring is simple artinian. We also describe the structure of an indecomposable right artinian right non-singular right a-ring as a triangular matrix ring of certain block matrices. (C) 2015 Elsevier B.V. All rights reserved.