Soft normed rings

Area of Science:

• Mathematics
• Abstract Algebra
• Set Theory

Background:

• Uncertainty is a significant challenge in various scientific fields.
• Soft set theory, introduced by Molodtsov, offers a novel framework for modeling imprecise information.
• Existing algebraic structures often lack robust methods for handling uncertainty.

Purpose of the Study:

• To initiate the study of soft normed rings by integrating soft set theory with algebraic structures.
• To extend the concepts of normed rings to the soft set environment.
• To explore the fundamental properties and characteristics of these new mathematical objects.

Main Methods:

• Application of soft set theory to the definition of normed rings.
• Development of definitions for soft normed rings, soft normed ideals, and soft complete normed rings.
• Investigation of theoretical properties and illustration with examples.

Main Results:

• Formal introduction of the concept of soft normed rings.
• Definition and exploration of soft normed ideals within this framework.
• Establishment of the notion of soft complete normed rings.
• Presentation of relevant properties and illustrative examples.

Conclusions:

• Soft set theory provides a viable tool for developing new algebraic structures that handle uncertainty.
• The introduced concepts of soft normed rings and ideals offer a foundation for future research in this area.
• This work lays the groundwork for applying soft set theory to other areas of abstract algebra.