ASSOCIATIVE NIL-ALGEBRAS OVER FINITE FIELDS

作者：Lopatin Artem A^*; Shestakov Ivan P

来源：International Journal of Algebra and Computation, 2013, 23(8): 1881-1894.

DOI：10.1142/S0218196713500471

• Nil-algebras
• nilpotency degree
• Nagata-Higman theorem
• PI-algebras
• associative algebras
• finite fields

We study the nilpotency degree of a relatively free finitely generated associative algebra with the identity x(n) = 0 over a finite field F with q elements. In the case of q >= n the nilpotency degree is proven to be the same as in the case of an infinite field of the same characteristic. In the case of q = n - 1 it is shown that the nilpotency degree differs from the nilpotency degree for an infinite field of the same characteristic by at most one. The nilpotency degree is explicitly computed for n = 3.

• 出版日期2013-12