Applications of Soft Union Sets in the Ring Theory

The aim of the paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of λ,μ-soft union rings which is a generalization of that of soft union rings is proposed. By intro...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2013-01, Vol.2013 (2013), p.709-717-371
Main Authors: Yang, Yongwei, Xin, Xiao Long, He, Pengfei
Format: Article
Language:English
Subjects:
Algebra
Banking industry
Credit reports
Fair Credit Reporting Act 1970-US
Foundations
Fuzzy logic
Fuzzy sets
Invariants
Mathematical analysis
Mathematical research
Quotients
Rings (Algebra)
Rings (mathematics)
Set theory
Unions
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Summary:The aim of the paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of λ,μ-soft union rings which is a generalization of that of soft union rings is proposed. By introducing the notion of soft cosets, soft quotient rings based on λ,μ-soft union ideals are established. Moreover, through discussing quotient soft subsets, an approach for constructing quotient soft union rings is made. Finally, isomorphism theorems of λ,μ-soft union rings related to invariant soft sets are discussed.
ISSN:1110-757X
1687-0042
DOI:10.1155/2013/474890