On semiperfect $a$-rings
UDC 512.5 A ring is  called a right $a$-ring if  every right ideal is automorphism invariant.  We describe some properties of $a$-rings over  semiperfect rings.   It is shown that an  I-finite right $a$-ring&a...
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| Datum: | 2024 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2024
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7491 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 512.5
A ring is  called a right $a$-ring if  every right ideal is automorphism invariant.  We describe some properties of $a$-rings over  semiperfect rings.   It is shown that an  I-finite right $a$-ring  is a direct sum of a semisimple Artinian ring and a basic ring. It is also demonstrated that if $R$ is  an indecomposable (as a ring) I-finite right $a$-ring not  simple with nontrivial idempotents  such that  every minimal right ideal  is a right annihilator and  ${\rm Soc}(R_R)={\rm Soc}(_RR)$  is essential in $R_R$, then $R$ is a quasi-Frobenius ring and it is also  a right $q$-ring.  |
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| DOI: | 10.3842/umzh.v76i5.7491 |