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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| Дата: | 2025 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2025
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2396 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-23962025-10-27T20:24:52Z On algebras that are sums of two subalgebras Kępczyk, Marek rings with polynomial identities, left T-nilpotent rings, prime rings 16D25, 16R10, 16N40 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. Lugansk National Taras Shevchenko University 2025-10-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2396 10.12958/adm2396 Algebra and Discrete Mathematics; Vol 40, No 1 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2396/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2396/1301 Copyright (c) 2025 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2025-10-27T20:24:52Z |
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OJS |
| language |
English |
| topic |
rings with polynomial identities left T-nilpotent rings prime rings 16D25 16R10 16N40 |
| spellingShingle |
rings with polynomial identities left T-nilpotent rings prime rings 16D25 16R10 16N40 Kępczyk, Marek On algebras that are sums of two subalgebras |
| topic_facet |
rings with polynomial identities left T-nilpotent rings prime rings 16D25 16R10 16N40 |
| format |
Article |
| author |
Kępczyk, Marek |
| author_facet |
Kępczyk, Marek |
| author_sort |
Kępczyk, Marek |
| title |
On algebras that are sums of two subalgebras |
| title_short |
On algebras that are sums of two subalgebras |
| title_full |
On algebras that are sums of two subalgebras |
| title_fullStr |
On algebras that are sums of two subalgebras |
| title_full_unstemmed |
On algebras that are sums of two subalgebras |
| title_sort |
on algebras that are sums of two subalgebras |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2025 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2396 |
| work_keys_str_mv |
AT kepczykmarek onalgebrasthataresumsoftwosubalgebras |
| first_indexed |
2025-10-26T02:08:37Z |
| last_indexed |
2025-10-28T02:44:44Z |
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1849545202377687040 |