57
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Nonfinitely Based Varieties of Right Alternative Metabelian Algebras

Pages 3169-3189 | Received 08 Feb 2014, Published online: 04 Jun 2015

REFERENCES

  • Belkin , V. P. ( 1976 ). Varieties of right alternative algebras . Algebra Logic 15 : 309 – 320 .
  • Belov , A. Ya. ( 2000 ). Counterexamples to the Specht problem . Sb. Math. 191 : 329 – 340 .
  • Drensky , V. S. ( 1974 ). On identities of Lie algebras . Algebra Logic 13 : 150 – 165 .
  • Grishin , A. V. ( 1999 ). Examples of infinitely based T-spaces and T-ideals in characteristic 2 . Fundam. Prikl. Mat. 5 : 101 – 118 (Russian) .
  • Il'tyakov . A. V. ( 1991 ). Finiteness of basis of identities of a finitely generated alternative PI–algebra over a field of characteristic zero . Sib. Math. J. 32 : 948 – 961 .
  • Il'tyakov , A. V. ( 1992 ). On finite basis of identities of Lie algebra representations . Nova J. Algebra Geom. 1 : 207 – 259 .
  • Isaev , I. M. ( 1986 ). Finite–dimensional right alternative algebras that do not generate finitely based varieties . Algebra Logic 25 : 86 – 96 .
  • Kemer , A. R. ( 1987 ). Finite basis property of identities of associative algebras . Algebra Logic 26 : 362 – 397 .
  • Kemer , A. ( 1988 ). Ideals of identities of associative alqebras . In: AMS Translations of Mathematical Monograph , Vol. 87 .
  • Kuz'min , A. M. ( 2008 ). On Spechtian varieties of right alternative algebras . J. Math. Sci. 149 : 1098 – 1106 .
  • Medvedev , Yu. A. ( 1978 ). Finite basis theorem for varieties with a two-term identity . Algebra Logic 17 : 458 – 472 .
  • Medvedev , Yu. A. ( 1980 ). Example of a variety of solvable alternative algebras over a field of characteristic 2 having no finite basis of identities . Algebra Logic 19 : 191 – 201 .
  • Pchelintsev , S. V. ( 1982 ). Varieties of algebras that are solvable of index 2 . Math. USSR Sb. 43 : 159 – 180 .
  • Pchelintsev , S. V. ( 2000 ). An almost Spechtian variety of alternative algebras over a field of characteristic 3 . Sb. Math. 191 : 909 – 925 .
  • Pchelintsev , S. V. ( 2001 ). The structure of weak identities on the Grassmann envelopes of central-by-metabelian alternative superalgebras of superrank 1 over a field of characteristic 3 . Fundam. Prikl. Mat. 7 : 849 – 871 (Russian) .
  • Pchelintsev , S. V. (2005). Grassmann right alternative metabelian algebras. XIII International conference “Math. Economi. Education” III Unternational symposium “Fourier series and applications.” Abstracts. p. 87. Rostov upon Don. 2005. ISBN 5–94153–097–8 (Russian).
  • Pchelintsev , S. V. ( 2008 ). On identities of right alternative metabelian Grassmann algebras . J. Math. Sci. 154 : 230 – 248 .
  • Schigolev , V. V. ( 2000 ). Examples of T-spaces with an infinite basis . Sb. Math. 191 : 459 – 476 .
  • Shestakov , I. P. ( 1991 ). Superalgebras and counterexamples . Sib. Math. J. 32 : 1052 – 1060 .
  • Shestakov , I. P. ( 1993 ). Prime Mal'tsev superalgebras . Math. USSR Sb. 74 : 101 – 110 .
  • Specht , W. ( 1950 ). Gesetze in Ringen . Math. Zeits. 52 : 557 – 589 .
  • Umirbaev , U. U. ( 1984 ). Metabelian binary–Lie algebras . Algebra Logic 23 : 155 – 160 .
  • Umirbaev , U. U. ( 1985 ). Specht varieties of soluble alternative algebras . Algebra Logic 24 : 140 – 149 .
  • Vais , A. Ya. , Zel'manov , E. I. ( 1989 ). Kemer's Theorem for finitely generated Jordan algebras . Sov. Math. 33 : 38 – 47 .
  • Vaughan–Lee , M. R. ( 1968 ). Some varieties of Lie algebras. D. Phil. dissertation, Oxford .
  • Vaughan–Lee , M. R. ( 1970 ). Varieties of Lie algebras . Quart. J. Math. 21 : 297 – 308 .
  • Vaughan–Lee , M. ( 1998 ). Superalgebras and dimensions of algebras . Int. J. Algebra Comput. 8 : 97 – 125 .
  • Zel'manov , E. I. , Shestakov , I. P. ( 1991 ). Prime alternative superalgebras and nilpotentcy of the radical of a free alternative algebra . Math. USSR Izv. 37 : 19 – 36 .
  • Zhevlakov , K. A. , Slin'ko , A. M. , Shestakov , I. P. , Shirshov , A. I. ( 1982 ). Rings That Are Nearly Associative . New York : Academic Press .
  • Communicated by A. Elduque.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.