| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2023-04-20T13:46:25Z |
| Last updated:
|
2025-01-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151643 |
| . |
| Reference:
|
[1] Fuchs L.: Abelian Groups.Springer Monographs in Mathematics, Springer, Cham, 2015. Zbl 1265.06054, MR 3467030 |
| 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 |
| . |
