Definition 1. An element a of a pseudo-normed ring (R; ») is called: topologically nilpotent if for any positive real number " there exists a positive integer n such that » ¡ ai ¢ < " for any positive integer i ¸ n; generalized nilpotent if limk!1( k p »(ak)) = 0, i.e., if for any positive real number " there exists a positive integer n such that » ¡ ai ¢ < "i for any positive integer i ¸ n. Definition 2. If (R; ») is a pseudo-normed ring and p is a nonnegative real number, then an element a of the pseudonormed ring (R; ») is called generalized nilpotent of degree p if for any positive real number " there exists a positive integer n such that » ¡ ai ¢ < "ip for any positive integer i ¸ n. Properties of generalized nilpotent elements of pseudo-normed commutative rings are studied in [1, 2]. Remark. Definitions 1 and 2 easily imply the following statements: 1. An element a of a pseudo-normed ring (R; ») is generalized nilpotent of degree 0 if and only if the element a is a topologically nilpotent element; 2. If p and q are real numbers such that 0 · p < q, then any element of a pseudo-normed ring (R; ») which is generalized nilpotent of degree q is generalized nilpotent of degree p. Theorem. If (R; ») is a pseudo-normed ring then for any real number 0 · r < 1 any topologically nilpotent element of the pseudo-normed ring (R; ») is a generalized nilpotent element of degree r.