A result on generalized derivations with engel conditions on one-sided ideals

Let R be a non-commutative prime ring and I a non-zero left ideal of R. Let U be the left Utumi quotient ring of R and C be the center of U and k, m, n, r fixed positive integers. If there exists a generalized derivation g of R such that [g(xm)xn, xr]k = 0 for all x Ie{cyrillic, ukrainian} I, then there exists a Ie{cyrillic, ukrainian} U such that g(x) = xa for all x Ie{cyrillic, ukrainian} R except when R = M2(GF(2)) and I[I, I] = 0. © 2010 The Korean Mathematical Society

Small sample properties of tests on homogeneity in one—way Anova and Meta—analysis

meta—analysis, balanced and unbalanced sample sizes, homogeneous and heterogeneous variances, nonnormality,