Unit lifting morphisms

Özarslan M., ÖZCAN A.

Expositiones Mathematicae, vol.40, no.3, pp.456-468, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1016/j.exmath.2022.03.003
  • Journal Name: Expositiones Mathematicae
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.456-468
  • Keywords: Unit lifting morphism, Local morphism, Local ring, Semilocal ring
  • Hacettepe University Affiliated: Yes

Abstract

© 2022 Elsevier GmbHIn this paper, we introduce the concept of a unit lifting morphism, a natural generalization of the classical notion “local morphism”, by providing several examples and investigating all its properties and interrelations with local morphisms and unit lifting ideals. Moreover, we expose a relation between a unit lifting morphism f:R→S of rings and the pair (ker(f),f−1(U(S))) and show that unit lifting morphisms correspond to the least element of a partially ordered set. As a prominent result, we provide the equivalent conditions on the existence of a unit lifting morphism from a ring R into a semisimple artinian ring which is intimately related to a deep result by Camps and Dicks that characterizes semilocal rings in terms of local morphisms. This result gives rise to the study of a new class of rings, which we call weakly semilocal rings.