66
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

GRADED IDENTITIES AND PI EQUIVALENCE OF ALGEBRAS IN POSITIVE CHARACTERISTIC

, &
Pages 1011-1022 | Received 13 Nov 2003, Accepted 26 Jul 2004, Published online: 23 Jul 2010

REFERENCES

  • Azevedo , S. S. ( 2002 ). Graded identities for the matrix algebra of order n over an infinite field . Commun. Alg. 30 ( 12 ): 5849 – 5860 .
  • Azevedo , S. S. ( 2003 ). A basis for ℤ-graded identities of matrices over infinite fields . Serdica 29 : 149 – 158 .
  • Azevedo , S. S. , Fidelis , M. , Koshlukov , P. ( 2004 ). Tensor product theorems in positive characteristic . J. Alg. 276 ( 2 ): 836 – 845 . [CROSSREF]
  • Bahturin , Yu. , Giambruno , A. , Zaicev , M. ( 1998 ). Codimension growth and graded identities . Alg. (Moscow) 57 – 76 ; Berlin : de Gruyter 2000 .
  • Berele , A. ( 1993 ). Generic verbally prime algebras and their GK-dimensions . Commun. Alg. 21 ( 5 ): 1487 – 1504 .
  • Chiripov , P. Zh., Siderov , P. N. ( 1981 ). On bases for identities of some varieties of associative algebras (in Russian) . Pliska Stud. Math. Bulgar. 2 : 103 – 115 .
  • Colombo , J. , Koshlukov , P. ( 2004 ). Central polynomials in the matrix algebra of order two . Linear Alg. Appl. 377 : 53 – 67 . [CROSSREF]
  • Di Vincenzo , O. M. ( 1992 ). On the graded identities of M1, 1( E) . Israel J. Math. 80 ( 3 ): 323 – 335 .
  • Di Vincenzo , O. M. , Nardozza , V. ( 2003 ). Graded polynomial identities for tensor products by the Grassmann algebra . Commun. Alg. 31 ( 3 ): 1453 – 1474 . [CROSSREF]
  • Di Vincenzo , O. M. , Nardozza , V. ( 2002 ). ℤ. k +l×ℤ2-graded polynomial identities for Mk, l(E) ⊗ E . Rend. Sem. Mat. Univ. Padova 108 : 27 – 39 .
  • Drensky , V. ( 1980 ). A minimal basis for the identities of a second-order matrix algebra over a field of characteristic 0 . Alg. Logic 20 : 188 – 194 .
  • Kemer , A. ( 1991 ). Ideals of identities of associative algebras . Translations Math. Monographs 87 . Providence , RI : Am. Math. Soc. .
  • Koshlukov , P. ( 2001 ). Basis of the identities of the matrix algebra of order two over a field of characteristic . p  ≠ 2. J. Alg. 241 : 410 – 434 .
  • Koshlukov , P. , Azevedo , S. S. ( 2002 ). Graded identities for . T -prime algebras over fields of positive characteristic. Israel J. Math. 128 : 157 – 176 .
  • Krakowski , D. , Regev , A. ( 1973 ). The polynomial identities of the Grassmann algebra . Trans. Am. Math. Soc. 181 : 429 – 438 .
  • Popov , A. ( 1982 ). Identities of the tensor square of a Grassmann algebra . Alg. Logic 21 : 296 – 316 .
  • Razmyslov , Yu. P. ( 1973 ). Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero . Alg. Logic 10 : 47 – 63 .
  • Razmyslov , Yu. P. ( 1994 ). Identities of algebras and their representations. Translations Math. Monographs 138. Providence, RI: Am. Math. Soc. .
  • Regev , A. ( 1990 ). Tensor products of matrix algebras over the Grassmann algebra . J. Alg. 133 ( 2 ): 512 – 526 . [CROSSREF]
  • Regev , A. ( 1991 ). Grassmann algebras over finite fields . Commun. Alg. 19 : 1829 – 1849 .
  • Stojanova-Venkova , A. H. ( 1980 ). Bases of identities of Grassmann algebras (in Russian) . Serdica 6 ( 1 ): 63 – 72 .
  • Vasilovsky , S. Yu. ( 1998 ). ℤ-graded polynomial identities of the full matrix algebra . Commun. Alg. 26 ( 2 ): 601 – 612 .
  • Vasilovsky , S. Yu. ( 1999 ). ℤn-graded polynomial identities of the full matrix algebra of order n . Proc. Am. Math. Soc. 127 ( 12 ): 3517 – 3524 . [CROSSREF]
  • #Communicated by R. Parimala.

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.