The p.p. property of trivial extensions


Kosan M. T.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.14, no.8, 2015 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 8
  • Publication Date: 2015
  • Doi Number: 10.1142/s0219498815501248
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Keywords: Left p.p.-ring, formal triangular matrix ring, trivial Morita context, trivial extension, MORITA CONTEXTS

Abstract

In this note, a necessary and sufficient condition for a trivial extension to be a left p.p.-ring is obtained. As an application, we determine when a trivial Morita context is a left p.p.-ring, and a result of Xue [On p.p. rings, Kobe J. Math. 7 (1990) 77-80] characterizing triangular p.p.-rings follows immediately.