On the nonexistence of hypercommuting polynomials
Copyright policy )On the nonexistence of hypercommuting polynomials
If f ( x 1 , … , x n ) f({x_1}, \ldots ,{x_n}) is not central for R, then the additive group generated by all specializations of f in R contains a noncentral Lie ideal of R. This is used, among other things, to prove: Theorem. Let R be a semiprime algebra over an infinite field, f 1 , … , f t {f_1}, \ldots ,{f_t} polynomials in disjoint sets of variables all noncentral for R. Then, if R satisfies S t [ f 1 , … , f t ] {S_t}[{f_1}, \ldots ,{f_t}] , R must satisfy S t [ x 1 , … , x t ] {S_t}[{x_1}, \ldots ,{x_t}] .
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Prime and semiprime associative rings, Rings with polynomial identity, Endomorphism rings; matrix rings, Center, normalizer (invariant elements) (associative rings and algebras)
Prime and semiprime associative rings, Rings with polynomial identity, Endomorphism rings; matrix rings, Center, normalizer (invariant elements) (associative rings and algebras)
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