Codimension On PI-Algebra

For PI algebra codimension of the discussion is mainly focused on the boundedness of the proof, the general PI-algebra codimension, according to its concept, we have cn(A)≤n! and Amital Regev in his doctoral thesis prove that any two PI-algebraic tensor product is still the PI-algebra in the process of the discussion about the codimension and presents a more precise conclusion cn(A)≤(3·4d-3)n in which d to meet the number of the multiple linear algebraic identities.And this paper use the method of Amitsur table proved satisfy multiple linear equation g(x) d times PI-algebra φ{X}/I and it’s codimension cn(φ{X}/I)≤(d-1)2n, proof of this conclusion does not have too much to discuss polynomial, but instead, codimension on the relative freedom algebra gives more accurate results. Besides this paper on the basis of using the method of multiple linear polynomial to the condition of the theorem of the multiple linear simplified processing,which is the corollary1In addition, cn(A) with the increase of n into power exponential growth, the growth rate of codimension series exp(A)=lim(?) Giambruno-Zaicev theorem has proved that exp(A) existence and the result is always positive integer, Auan and Amitai proved exp(f)≤[deg f/2]2, and this article will further discuss when n is large enough to its strictness exp(f)<[deg f/2]2is established.