On algebras that are sums of two subalgebras
We study an associative algebra \(A\) over an arbitrary field \(K\) that is a sum of two subalgebras \(B\) and \(C\) (i.e. \(A=B+C)\). Let \(\mathcal{M}\) be the class of algebras such that \(B, C\in \mathcal{M}\) implies \(A\in \mathcal{M}\). We prove, under some natural additional assumptions on \...
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| Datum: | 2025 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2025
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2396 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | We study an associative algebra \(A\) over an arbitrary field \(K\) that is a sum of two subalgebras \(B\) and \(C\) (i.e. \(A=B+C)\). Let \(\mathcal{M}\) be the class of algebras such that \(B, C\in \mathcal{M}\) implies \(A\in \mathcal{M}\). We prove, under some natural additional assumptions on \(\mathcal{M}\), that if \(B\) and \(C\) have ideals of finite codimension from \(\mathcal{M}\), then \(A\) has an ideal of finite codimension from \(\mathcal{M}\), too. In particular we show that if \(B\) and \(C\) have left T-nilpotent ideals (or nil \(PI\) ideals) of finite codimension, then \(A\) has a left T-nilpotent ideal (or nil \(PI\) ideal) of finite codimension. |
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