43 - M. Behboodi (Joint with G. Behboodi Eskandari) Local duo-rings whose finitely generated modules are direct sums of cyclics, Indian J. Pure and Appl. Math. (Accepted) (ISI)
In this paper, we give an answer to the following question of I. Kaplansky in the local case: For which duo rings R is it true that every nitely generated left R-module can be decomposed as a direct sum of cyclic modules? More precisely, we prove that for a local duo ring R, the following are equivalent: (i) Every nitely generated left R-module is a direct sum of cyclic modules; (ii) Every 2-generated left R-module is a direct sum of cyclic modules; (iii) Every factor module of RR R is a direct sum of cyclic modules; (iv) Every factor module of RR R is serial; (v) Every nitely generated left R-module is serial; (vi) R is uniserial and for every non-zero ideal I of R, R=I is a linearly compact left R-module; (vii) R is uniserial and every indecomposable injective left R-module is left uniserial; and, (viii) Every nitely generated right R-module is a direct sum of cyclic modules.