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The Study of Ring Theory : Fundamental Concepts, Applications, and Future Direction

  • Unique Paper ID: 166287
  • Volume: 11
  • Issue: 2
  • PageNo: 389-395
  • Abstract:
  • Ring theory, a cornerstone of abstract algebra, investigates algebraic structures known as rings, encompassing fundamental concepts like operations, ideals, modules, and homomorphisms. This paper provides a comprehensive examination of ring theory, emphasizing its role as a foundational concept in algebraic studies. Beginning with the basic definitions and algebraic properties of rings, the paper explores their applications across diverse disciplines such as algebraic geometry, coding theory, cryptography, and number theory. It highlights the significance of ring theory in constructing algebraic structures like polynomial rings and integral domains, essential for theoretical advancements and practical implementations. Furthermore, the paper discusses advanced topics within ring theory, including commutative and non-commutative algebra, homological methods, and computational aspects. It identifies current challenges and open problems within the field, suggesting potential avenues for future research to expand the theoretical framework and enhance practical applications of ring theory.
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Cite This Article

  • ISSN: 2349-6002
  • Volume: 11
  • Issue: 2
  • PageNo: 389-395

The Study of Ring Theory : Fundamental Concepts, Applications, and Future Direction

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Journal no 47859

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