NON-PARALLEL KRULL DIMENSION OF MODULES

Document Type : Original Manuscript

Authors

Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

10.22044/jas.2024.14545.1841

Abstract

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.

Keywords

References

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Journal of Algebraic Systems
Volume 14, Issue 3
June 2026
Pages 407-425

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