| Title:
|
Infinite independent systems of the identities of the associative algebra over an infinite field of characteristic $p>0$ (English) |
| Author:
|
Sandu, N. I. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
1-23 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper some infinitely based varieties of groups are constructed and these results are transferred to the associative algebras (or Lie algebras) over an infinite field of an arbitrary positive characteristic. (English) |
| Keyword:
|
associative algebras |
| Keyword:
|
infinite systems of identities |
| Keyword:
|
Specht’s problem. |
| MSC:
|
16R10 |
| MSC:
|
20E10 |
| idZBL:
|
Zbl 1081.16030 |
| idMR:
|
MR2121653 |
| . |
| Date available:
|
2009-09-24T11:20:32Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127956 |
| . |
| Reference:
|
[1] W. Specht: Gesetze in Ringen 1.Math. Z. 52 (1950), 557–589. MR 0035274, 10.1007/BF02230710 |
| Reference:
|
[2] A. P. Kemer: Finite basing of the identities of the associative algebras.Algebra i logika 26 (1987), 597–641. (Russian) MR 0985840, 10.1007/BF01978692 |
| Reference:
|
[3] V. V. Schigolev: Examples of infinitely based $T$-spaces.Matem. sb. 191 (2000), 143–160. (Russian) MR 1773258 |
| Reference:
|
[4] A. I. Belov: Counterexamples to the Specht’s problem.Matem. sb. 191 (2000), 13–24. (Russian) MR 1773251 |
| Reference:
|
[5] N. I. Sandu: Infinite independent systems of the identities of the associative algebras over an infinite field of characteristic 2.Matem. zametki 74 (2003), 603–611. (Russian) MR 2042973 |
| Reference:
|
[6] : The Dnestr Notebook. Unsolved Problems of the Ring and Module Theory.Institute of Mathematics of SD AS USSS, Novosibirsk, 1982. (Russian) |
| Reference:
|
[7] A. E. Zalesskij and A. V. Mikhalev: Group rings. The results of science and technique.Modern Mathematics Problems. Main Directions, VINITI, Moskva, 1973, pp. 5–118. (Russian) MR 0414623 |
| Reference:
|
[8] M. R. Vaughan-Lee: Uncountably many varieties of groups.Bull. London Math. Soc. 2 (1970), 280–286. Zbl 0216.08401, MR 0276307, 10.1112/blms/2.3.280 |
| Reference:
|
[9] S. Leng: Algebra.Addison-Wesley Publishing Company, Reading, 1965. MR 0197234 |
| Reference:
|
[10] W. Magnus, A. Karrass and D. Solitar: Combinatorial Group Theory.Wiley, New York, 1966. |
| Reference:
|
[11] M. R. Vaughan-Lee: Varieties of Lie algebras.Quart. J. Math. 21 (1970), 297–308. Zbl 0204.35901, MR 0269710, 10.1093/qmath/21.3.297 |
| Reference:
|
[12] V. S. Drenski: About identities in Lie algebras.Algebra i logika 13 (1974), 265–290. (Russian) MR 0374220, 10.1007/BF01463349 |
| . |
