Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra Ur,s(sl2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{

Let U be the two-parameter quantized enveloping algebra Ur,s(sl2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${U_{r,s}}({\mathfrak{s}\mathfrak{l}_2})$$\end{document} and F(U) the locally finite subalgebra of U under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of F(U) in the case when rs−1 is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of U by generators.