Unit lifting morphisms

Özarslan M., ÖZCAN A.

Expositiones Mathematicae, cilt.40, sa.3, ss.456-468, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.exmath.2022.03.003
  • Dergi Adı: Expositiones Mathematicae
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.456-468
  • Anahtar Kelimeler: Unit lifting morphism, Local morphism, Local ring, Semilocal ring
  • Hacettepe Üniversitesi Adresli: Evet

Özet

© 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.