Endomorphism Rings Via Minimal Morphisms

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

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.18, sa.4, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s00009-021-01802-9
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Endomorphism ring, Ziegler partial morphism, approximations, automorphism-invariant, INVARIANT
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.