Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 1 2026 01 01 ON TYPE KRULL DIMENSION OF MODULES 29 44 3134 10.22044/jas.2024.14020.1789 EN Nasrin Shirali Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. Hooriya Kavoosi Ghafi Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. Sayed Malek Javdannezhad Department of Mathematics, Shahid Rajaee Teacher Training University, Tehran, Iran. Journal Article 2024 01 01 In this paper, the concept of type Krull dimension of a module is introduced and some related properties are investigated.<br />Using this concept, we extend some basic results about modules with Krull dimension. It is shown that every module with homogeneous type Krull dimension has type Krull dimension equal to zero. Also, it is proved that an $R$-module $M$ has type Krull dimension if and only if it has type Noetherian dimension. We observe that, every module with Krull dimension has type Krull dimension, but its converse is not true in general. Further, we define t-Artinian (resp., t-Noetherian) modules and it is shown that if $M$ be a t-Artinian $R$-module with type Krull dimension, then it has Krull dimension and these two dimensions for $M$ coincide. At the end, we define the concept of $\alpha$-DICCT modules and it is proved that an $R$-module $M$ is $\alpha$-DICCT if and only if it has type Krull dimension. https://jas.shahroodut.ac.ir/article_3134_61b00cde6ade023d5f939f306c9abcfd.pdf