We describe the ring of constants of a specific four variable Lotka-Volterra derivation. We investigate the existence of polynomial constants in the other cases of Lotka-Volterra derivations, also in n variables.
The notion of a closed polynomial over a field of zero characteristic was introduced by Nowicki and Nagata. In this paper we discuss possible ways to define an analog of this notion over fields of positive characteristic. We are mostly interested in conditions of maximality of the algebra generated by a polynomial in a respective family of rings. We also present a modification of the condition of integral closure and discuss a condition involving partial derivatives.