On the primality property of central polynomials of prime varieties of associative algebras

Аннотация

In the paper, it is proved that, if f(x₁,..., x_n)g(y₁,..., y_m) is a multilinear central polynomial for a verbally prime T-ideal Γ over a field of arbitrary characteristic, then both polynomials f(x₁,..., x_n) and g(y₁,..., y_m) are central for Γ.