We define and study a new dimension , which we call uniserial dimension . This ordinal valued dimension is a measure of how far a module deviates from being uniserial . Noetherian modules are a We characterize rins whose modules have uniserial dimension . Uniserial dimension of modules over commutative rings are considered specially. W e show that the commutative rings of finite uniserial dimension strictly lies between the Duality , we define and study couniserial dimension for modules . Couniserial dimension is a measure of how far a module deviates from being uniform . Each module having such a dimension contains a uniform submodule and every module of finite couniserial dimension has finite uniform dimension . Every module of finite length has couniserial dimension and its value lies between the uniform dimension and the length of the module . As one of the applications , it follows that all right R-modules have couniserial dimension if and only if R is a semisimple Artinian ring .
