A class of rings with the 2-sum property


KOŞAN M. T. , Zhou Y.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol.32, no.3, pp.399-408, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1007/s00200-021-00490-y
  • Journal Name: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.399-408
  • Keywords: Unit, Binary 2-sum property, Semilocal ring
  • Gazi University Affiliated: Yes

Abstract

Recall that a ring satisfies the 2-sum property if each of its elements is a sum of two units. Here a ring R is said to satisfy the binary 2-sum property if, for any a, b in R, there exists a unit u of R such that both a - u and b - u are units. A well-known result, due to Goldsmith, Pabst and Scot, states that a semilocal ring satisfies the 2-sum property iff it has no image isomorphic to Z(2). It is proved here that a semilocal ring satisfies the binary 2-sum property iff it has no image isomorphic to Z(2) or Z(3) or M-2(Z(2))