Double centralizers of minimal faithful modules over left serial algebras (Q1068916)

An algebra A is said to be QF-1 if every finitely generated faithful A- module is balanced. \textit{R. M. Thrall} [Trans. Am. Math. Soc. 64, 173-183 (1948; Zbl 0041.010)] proposed to give an ideal theoretical characterization of QF-1 algebras, but this problem remains unsolved at the present except for serial algebras, local algebras and algebras with radical square zero. The author calls an algebra A to be weakly QF-1 if every minimal faithful A-module is balanced. He obtains a sufficient condition for A to be weakly QF-1 and, applying the results concerning weakly QF-1 algebras, he gives a solution of Thrall's problem to the case of left serial algebras.