Abstract
In this paper, the concept of iso-DICC modules is introduced and extensively investigated. These modules are the generalization of DICC, iso-Noetherian and iso-Artinian modules. We prove that any direct sum of a projective iso-simple and an iso-DICC module is iso-DICC. Unlike DICC rings, we show that iso-DICC rings don’t have finite Goldie dimension, but if R is a semiprime right iso-DICC ring and I is an annihilator ideal of R, then either I or R I has finite Goldie dimension. Furthermore, we investigate the Krull dimension of iso-Noetherian modules and we give an answer to an open problem on this topic. Finally, we generalize some results on semiprime right iso-Artinian rings to a certain class of iso-Artinian modules. We provide sufficient conditions for iso-Artinian modules to have finite Goldie dimension. Also, we show that any semiprime FQS iso-Artinian module, is non-M-singular.
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