Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 3 2026 06 01 NON-PARALLEL KRULL DIMENSION OF MODULES 407 425 3819 10.22044/jas.2024.14545.1841 EN Nasrin Shirali Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. Mohammad Maschizadeh Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. Journal Article 2024 05 18 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 $. <br />Also, it is proved that any np-Noetherian $R$-module has non-parallel Krull dimension.<br />In particular, for semiprime right non-atomic rings, we show that Krull dimension and non-parallel Krull dimension coincide. https://jas.shahroodut.ac.ir/article_3819_bfedd4fb2ca0ef29f5dddb68835a21b0.pdf