Endomorphism Rings Via Minimal Morphisms

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 fr...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2021-08, Vol.18 (4), Article 152
Main Authors: Cortés-Izurdiaga, Manuel, Guil Asensio, Pedro A., Tütüncü, D. Keskin, Srivastava, Ashish K.
Format: Article
Language:English
Subjects:
Automorphisms
Invariants
Isomorphism
Mathematics
Mathematics and Statistics
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Summary: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 .
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-021-01802-9