Endomorphism Rings Via Minimal Morphisms


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

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.18, no.4, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.1007/s00009-021-01802-9
  • Title of Journal : MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Keywords: Endomorphism ring, Ziegler partial morphism, approximations, automorphism-invariant, INVARIANT

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.