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(α,β)-Soft Intersectional Rings and Ideals with their Applications

Author

Listed:
  • Chiranjibe Jana

    (Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore 721102, India)

  • Madhumangal Pal

    (Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore 721102, India)

  • Faruk Karaaslan

    (#x2020;Department of Mathematics, Faculty and Sciences, Çankırı Karatekin University, 18100 Çankırı, Turkey)

  • Aslihan Sezgi̇n

    (#x2021;Amasya University, Department of Elementary Mathematics, 05100 Amasya, Turkey)

Abstract

Molodtsov initiated the soft set theory, providing a general mathematical framework for handling uncertainties that we encounter in various real-life problems. The main object of this paper is to lay a foundation for providing a new soft algebraic tool for considering many problems that contain uncertainties. In this paper, we introduce a new kind of soft ring structure called (α,β)-soft-intersectional ring based on some results of soft sets and intersection operations on sets. We also define (α,β)-soft-intersectional ideal and (α,β)-soft-intersectional subring, and investigate some of their properties using these new concepts. We obtain some results in ring theory based on (α,β)-soft intersection sense and its application in ring structures. Furthermore, we provide relationships between soft-intersectional ring and (α,β)-soft-intersectional ring, soft-intersectional ideal and (α,β)-soft-intersectional ideal.

Suggested Citation

  • Chiranjibe Jana & Madhumangal Pal & Faruk Karaaslan & Aslihan Sezgi̇n, 2019. "(α,β)-Soft Intersectional Rings and Ideals with their Applications," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 333-350, July.
    • Handle: RePEc:wsi:nmncxx:v:15:y:2019:i:02:n:s1793005719500182
    DOI: 10.1142/S1793005719500182
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