نوع مقاله : مقاله پژوهشی
نویسندگان
1 ِDepartment of mathematics shahid chamran university of ahvaz , ahvaz iran
2 Shahid Rajaee Teacher Training University,
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسندگان [English]
In this paper, we first consider the concept of type Noetherian dimension of a module such as $M$, which is dual of the type Krull dimension, denoted by $\tndim\, (M)$, and defined to be the codeviation of the poset of the type submodules of $M$, then we dualize some basic results of type Krull dimension for type Noetherian dimension. In the following, we introduce the concept of $\alpha$-type short modules (i.e., for each type submodule $A$ of $M$, either $\ndim\, (\frac{M}{A})\leq \alpha$ or $\tndim\, (A)\leq \alpha$ and $\alpha$ is the least ordinal number with this property), and extend some basic results of $\alpha$-short modules to $\alpha$-type short modules. In particular, it is proved that if $M$ is an $\alpha$-type short module, then it has type Noetherian dimension and $\tndim\, (M)=\alpha$ or $\tndim\, (M)=\alpha+1$.
کلیدواژهها [English]
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