α-TYPE SHORT MODULES

Document Type : Original Paper

Authors

1 ِDepartment of mathematics shahid chamran university of ahvaz , ahvaz iran

2 Shahid Rajaee Teacher Training University,

Abstract

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 $\tndim\, (M)=\alpha+1$.

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Main Subjects

References

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History

  • Receive Date: 24 July 2024
  • Revise Date: 31 August 2024
  • Accept Date: 09 October 2024

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