Endomorphism Rings Via Minimal Morphisms

Creative Commons License

Cortes-Izurdiaga M., Guil Asensio P. A., Tutuncu D. K., Srivastava A. K.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.18, no.4, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.1007/s00009-021-01802-9
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Endomorphism ring, Ziegler partial morphism, approximations, automorphism-invariant, INVARIANT
  • Hacettepe University Affiliated: Yes

Abstract

We prove that if u : K -> M is a left minimal extension, then there exists an isomorphism between two subrings, End(R)(M) (K) and End(R)(K) (M) of End(R)(K) and End(R)(M), respectively, modulo their Jacobson radicals. This isomorphism is used to deduce properties of the endomorphism ring of K from those of the endomorphism ring of M in certain situations such us when K is invariant under endomorphisms of M, or when K is invariant under automorphisms of M.