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Soft ideals of soft ternary semigroups.

S Kar1, I Dutta1

  • 1Department of Mathematics, Jadavpur University, 188, Raja S. C. Mallick Road, Kolkata - 700032, India.

Heliyon
|June 30, 2021
PubMed
Summary

This study introduces soft ideals in soft ternary semigroups, exploring their relationships and using them to characterize completely regular soft ternary semigroups.

Keywords:
Soft bi-idealSoft completely regular ternary semigroupSoft irreducible idealSoft prime bi-idealSoft prime idealSoft semiprime bi-idealSoft semiprime idealSoft ternary semigroup

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Area of Science:

  • Algebraic structures
  • Abstract algebra
  • Soft set theory

Background:

  • Soft ternary semigroups are an extension of traditional algebraic structures.
  • Soft ideals are a key concept in generalizing ideal theory within these structures.
  • Understanding the properties of soft ideals is crucial for classifying semigroup types.

Purpose of the Study:

  • To introduce and define new classes of soft ideals in soft ternary semigroups.
  • To investigate the inter-relationships between various types of soft ideals.
  • To characterize completely regular soft ternary semigroups using these soft ideals.

Main Methods:

  • Definition of novel soft ideal classes within the soft ternary semigroup framework.
  • Analysis of the structural properties and interconnections of these soft ideals.
  • Application of soft ideal properties to establish criteria for completely regular soft ternary semigroups.

Main Results:

  • Several classes of soft ideals in soft ternary semigroups are formally introduced.
  • Key relationships and equivalences between different soft ideal types are established.
  • A characterization of completely regular soft ternary semigroups based on these soft ideals is provided.

Conclusions:

  • The introduced soft ideals offer a valuable tool for studying soft ternary semigroups.
  • The findings contribute to a deeper understanding of algebraic structures in soft set theory.
  • This work provides a foundation for further research into generalized ideal theory in abstract algebra.