Soft structures of groups and rings

Authors

  • Jayanta Ghosh

    Department of Mathematics,Manickpur Adarsha Vidyapith,Deltamill, Howrah-711309, West Bengal.

  • Dhananjoy Mandal

    Department of Mathematics, University of Calcutta, 35 Ballygunge circular road, Kolkata-700019.

  • Tapas Samanta

    Department of Mathematics, Uluberia College, Howrah-711315, West Bengal.

How to Cite

Ghosh, J., Mandal, D., & Samanta, T. (2017). Soft structures of groups and rings. International Journal of Scientific World, 5(2), 117-125. https://doi.org/10.14419/ijsw.v5i2.8012

Received date: June 18, 2017

Accepted date: August 7, 2017

Published date: August 29, 2017

DOI:

https://doi.org/10.14419/ijsw.v5i2.8012

Keywords:

Soft sets, Soft groups, Soft cosets, Soft rings, Soft integral domain.

Abstract

Concept of soft equivalence relations (classes, mappings) are introduced using the notion of soft elements. Then we redefine the notion of soft group and soft ring in a new way by using the idea of soft elements and it is seen that our definitions of soft group and soft ring are equivalent to the existing notions of soft group [2] and soft ring [1]. The notion of soft coset is presented and validated by suitable examples. We investigate some important properties like soft divisor of zero, characteristic of a soft ring etc. by considering examples. Moreover, some necessary and sufficient conditions are established for a soft ring to be a soft integral domain and soft field.

Author Biography

  • Jayanta Ghosh, Department of Mathematics,Manickpur Adarsha Vidyapith,Deltamill, Howrah-711309, West Bengal.
    Different algebraic structures in Soft set theory, Fuzzy set theory, Rough set theory and in their combinations.

References

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How to Cite

Ghosh, J., Mandal, D., & Samanta, T. (2017). Soft structures of groups and rings. International Journal of Scientific World, 5(2), 117-125. https://doi.org/10.14419/ijsw.v5i2.8012

Received date: June 18, 2017

Accepted date: August 7, 2017

Published date: August 29, 2017