Article
| Title: | Mal'tsev--Neumann products of semi-simple classes of rings (English) |
| Author: | Gardner, Barry James |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 63 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 415-421 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Malt'tsev--Neumann products of semi-simple classes of associative rings are studied and some conditions which ensure that such a product is again a semi-simple class are obtained. It is shown that both products, $\mathcal{S}_{1}\circ\mathcal{S}_{2}$ and $\mathcal{S}_{2}\circ\mathcal{S}_{1}$ of semi-simple classes $\mathcal{S}_{1}$ and $\mathcal{S}_{2}$ are semi-simple classes if and only if they are equal. (English) |
| Keyword: | radical class |
| Keyword: | semi-simple class |
| Keyword: | Mal'tsev--Neumann product |
| MSC: | 08C99 |
| MSC: | 16N80 |
| idZBL: | Zbl 07729551 |
| idMR: | MR4577039 |
| DOI: | 10.14712/1213-7243.2023.004 |
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| Date available: | 2023-04-20T13:46:25Z |
| Last updated: | 2023-10-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151643 |
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| Reference: | [2] Gardner B. J.: A note on Mal'tsev–Neumann products of radical classes.Int. Electron. J. Algebra 24 (2018), 1–11. MR 3828091, 10.24330/ieja.440117 |
| Reference: | [3] Gardner B. J., Wiegandt R.: Radical Theory of Rings.Monographs and Textbooks in Pure and Applied Mathematics, 261, Marcel Dekker, New York, 2004. MR 2015465 |
| Reference: | [4] Mal'tsev A. I.: Ob umnozhenii klassov algebraicheskikh sistem.Sibirskii Mat. Zh. 8 (1967), 346–365 (Russian). MR 0213276 |
| Reference: | [5] Neumann H.: Varieties of Groups.Springer, New York, 1967. Zbl 0251.20001, MR 0215899 |
| Reference: | [6] Penza T., Romanowska A. B.: Mal'tsev products of varieties, I..Algebra Universalis 82 (2021), no. 2, Paper No. 33, 19 pages. MR 4251619 |
| Reference: | [7] Snider R. L.: Subdirect decompositions of extension rings.Michigan Math. J. 16 (1969), 225–226. MR 0248177, 10.1307/mmj/1029000265 |
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