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

Chiranjibe Jana, Madhumangal Pal (), Faruk Karaaslan () and Aslihan Sezgi̇n ()
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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

New Mathematics and Natural Computation (NMNC), 2019, vol. 15, issue 02, 333-350

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.

Keywords: Ring; soft set; (α; β)-soft-intersectional ring; (α; β)-soft-intersectional ideal; soft (pre-)image (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S1793005719500182

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