FSFS neotherian and artinian modules

الملخص EN

Molodtsov [1] initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties.

Later other authors Maji et al.

[2-4] have further studied the theory of soft sets and also introduced the concept of fuzzy soft set, which is a combination of fuzzy set [5] and soft set.

Thereafter, Aktas and Cagman [6] have introduced the notion of soft groups.

Aygunoglu and Aygun [7] have generalized the concept of Aktas and Cagman [6] and introduce fuzzy soft group.

F.Feng et al.

[8] gave soft semirings and U.Acar et al.

[9] introduced initial concepts of soft rings.

Ghosh et al.

[10] gave the notion of fuzzy soft rings.

The definition of fuzzy modules is given by some authors.

[11-13] Qiu- Mei Sun et al.

[14] defined soft modules and investigated their basic properties.

Gunduz and Bayramov [15] introduced a basic version of fuzzy soft module theory.

Alhusiny A.

[16] gave the concept of modules.

In this paper the main purpose is to introduce a basic concept of Noetherian and Artinian.

and finally some of their basic properties.