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The Homomorphism Theorems of M -Hazy Rings and Their Induced Fuzzifying Convexities

Author

Listed:
  • Faisal Mehmood

    (Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China)

  • Fu-Gui Shi

    (Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China)

  • Khizar Hayat

    (School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510000, China
    Department of Mathematics and Big Data, Foshan University, Foshan 528000, China)

  • Xiao-Peng Yang

    (School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China)

Abstract

In traditional ring theory, homomorphisms play a vital role in studying the relation between two algebraic structures. Homomorphism is essential for group theory and ring theory, just as continuous functions are important for topology and rigid movements in geometry. In this article, we propose fundamental theorems of homomorphisms of M -hazy rings. We also discuss the relation between M -hazy rings and M -hazy ideals. Some important results of M -hazy ring homomorphisms are studied. In recent years, convexity theory has become a helpful mathematical tool for studying extremum problems. Finally, M -fuzzifying convex spaces are induced by M -hazy rings.

Suggested Citation

  • Faisal Mehmood & Fu-Gui Shi & Khizar Hayat & Xiao-Peng Yang, 2020. "The Homomorphism Theorems of M -Hazy Rings and Their Induced Fuzzifying Convexities," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:411-:d:332148
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    References listed on IDEAS

    as
    1. Fu-Gui Shi & Zhen-Yu Xiu, 2014. "A New Approach to the Fuzzification of Convex Structures," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, August.
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