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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| Veröffentlicht in: | Mediterranean journal of mathematics 2021-08, Vol.18 (4), Article 152 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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 |