On finite rings over which every free codes is splitting

In this paper, we study the structure of finite rings over which all free codes are splitting. In particular, we show that over the matrix rings over finite local rings all free codes are splitting

On nonsingular P-injective rings

A ring $R$ is said to be left $p$-injective if, for any principal left ideal $I$ of $R$, any left $R$-homomorphism $I$ into $R$ extends to one of $R$ into itself. In this note left nonsingular left $p$-injective rings are characterized using their maximal left rings of quotients and the structure of semiprime left $p$-injective rings of bounded index is investigated