NON-PARALLEL KRULL DIMENSION OF MODULES

In this paper, the concept of non-parallel Krull (resp., Noetherian) dimension of an R -module are introduced and some related properties are investigated. Using these concepts, we generalize some of the results of our previous work and sometimes obtain new results about np-Artinian (resp., np-Noetherian) modules. We give a characterization for modules with non-parallel Krull (resp., Noetherian) dimension and show that these modules have finite type dimension. It is shown that any R -module M with non-parallel Krull dimension at most \alpha is either atomic or \lambda -f.e. for some \lambda\leq\alpha . Also, it is proved that any np-Noetherian R-module has non-parallel Krull dimension.In particular, for semiprime right non-atomic rings, we show that Krull dimension and non-parallel Krull dimension coincide.

کلیدواژه ها:

non-parallel submodules ، atomic modules ، non-parallel Krull dimension ، non-parallel Noetherian dimension ، type dimension