53
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

A SIMPLE EXAMPLE OF A NON-FINITELY BASED SYSTEM OF POLYNOMIAL IDENTITIES

&
Pages 4851-4866 | Received 01 May 2001, Published online: 19 Aug 2006

References

  • Bakhturin , Yu.A. and Olshanskii , A.Yu. 1991 . “ Identities ” . In Algebra. II. Encyclopaedia of Mathematical Sciences Edited by: Kostrikin , A.I. and Shafarevich , I.R. Vol. 18 , 107 – 221 . Berlin : Springer-Verlag .
  • Belov , A.Ya. 1999 . On non-Specht Varieties . Fundam. Prikl. Mat. , 5 ( 1 ) : 47 – 66 . Russian
  • Belov , A.Ya. 2000 . Counterexamples to the Specht Problem . Mat. Sb. , 191 ( 3 ) : 13 – 24 .
  • 2000 . (Russian) English translation in Sb. Math. , 191 ( 3–4 ) : 329 – 340 .
  • Bokhut , L.A. , Lvov , I.V. and Kharchenko , V.K. 1991 . “ Noncommutative Rings ” . In Algebra. II. Encyclopaedia of Mathematical Sciences Edited by: Kostrikin , A.I. and Shafarevich , I.R. Vol. 18 , 1 – 106 . Berlin : Springer-Verlag .
  • Bryant , R.M. 1973 . Some Infinitely Based Varieties of Groups . J. Austral. Math. Soc. , 16 : 29 – 32 .
  • Drensky , V.S. 2000 . Free Algebras and PI-algebras xii+271 Singapore, , Singapore : Springer-Verlag .
  • Grishin , A.V. 1999 . Examples of T-spaces and T-ideals of Characteristic 2 without the Finite Basis Property . Fundam. Prikl. Mat. , 5 ( 1 ) : 101 – 118 . Russian
  • Grishin , A.V. 2000 . On Non-Spechtianness of the Variety of Associative Rings that Satisfy the Identity x32=0 . Electron. Res. Announc. Amer. Math. Soc. , 6 : 50 – 51 . electronic
  • Grishin , A.V. 2000 . “ The Variety of Associative Rings, which Satisfy the Identity x32=0, is not Specht ” . In In Formal Power Series and Algebraic Combinatorics 686 – 691 . Moscow : Springer . Berlin, 2000
  • Gupta , C.K. and Krasilnikov , A.N. 1995 . Some Non-finitely based Varieties of Groups and Group Representations . Internat. J. Algebra Comput. , 5 ( 3 ) : 343 – 365 .
  • Gupta , C.K. and Krasilnikov , A.N. 2001 . A Just Non-finitely Based Variety of Bigroups . Commun. Algebra , 29 ( 9 ) : 4011 – 4046 .
  • Kemer , A.R. 1987 . Finite Basability of Identities of Associative Algebras . Algebra i Logika , 26 ( 5 ) : 597 – 641 . Russian
  • Kemer , A.R. 1988 . Solution of the Problem as to Whether Associative Algebras have a Finite Basis of Identities . Dokl. Akad. Nauk SSSR , 298 ( 2 ) : 273 – 277 . Russian
  • 1988 . English Translation in Soviet Math. Dokl. , 37 ( 1 ) : 60 – 64 .
  • Kleiman , Yu.G. 1973 . On a Basis of the Product of Varieties of Groups . Izv. Akad. Nauk SSSR Ser. Mat. , 37 : 95 – 97 . Russian
  • 1973 . English Translation in Math. USSR-Izv. , 37 : 91 – 94 .
  • Krasilnikov , A.N. 1989 . Identities of Triangulable Matrix Representations of Groups . Trudy Moskov. Mat. Obshch. , 52 : 229 – 245 . Russian
  • 1990 . English Translation in Trans. Moscow Math. Soc. , : 233 – 249 . 1991
  • Newman , M.F. 1971 . Just Non-finitely-based Varieties of Groups . Bull. Austral. Math. Soc. , 4 : 343 – 348 .
  • Rowen , L.H. 1991 . Ring Theory xxviii+623 Boston, MA : Academic Press, Inc. .
  • Popov , A.P. 1979 . Some Finitely Based Varieties of Rings . C. R. Acad. Bulgare Sci. , 32 ( 7 ) : 855 – 858 .
  • Shchigolev , V.V. 1999 . Examples of Infinitely Based T-ideals . Fundam. Prikl. Mat. , 5 ( 1 ) : 307 – 312 . Russian
  • Shchigolev , V.V. 2000 . Examples of Infinitely Basable T-spaces . Mat. Sb. , 191 ( 3 ) : 143 – 160 . Russian
  • 2000 . English Translation in Sb. Math. , 191 ( 3–4 ) : 459 – 476 .
  • Vaughan-Lee , M.R. 1970 . Uncountably Many Varieties of Groups . Bull. London Math. Soc. , 2 : 280 – 286 .

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.