Soft Γ-Modules

Authors

  • Serkan Onar Yildiz Technical University, Department of Mathematics, Istanbul, Turkey
  • Sanem Yavuz Yildiz Technical University, Department of Mathematics, Istanbul, Turkey
  • Bayram Alì Ersoy Yildiz Technical University, Department of Mathematics, Istanbul, Turkey

DOI:

https://doi.org/10.23755/rm.v32i0.325

Keywords:

soft set, soft module, Γ- ring, Γ-module, soft Γ-module, soft Γ-module homomorphism, soft Γ-module isomorphism, soft Γ-exactness.

Abstract

In this paper, the denitions of soft  Γ-module, soft Γ-module homomorphism and soft Γ-exactness are introduced with the aid of the concept of soft set theory introduced by Molodtsov. In the meantime, some of their properties and structural characteristics are investigated and discussed. Thereafter, several illustrative examples are given.

References

D. Molodtsov, Soft set theory-First results, Computers Mathematics Applications, 37(4-5)(1999), 19-31.

P.K. Maji, A.R. Roy, R. Biswas, An application of soft sets in a decision making problem, Computers Mathematics Applications, 44(2002), 1077-1083.

D. Chen, E.C.C. Tsang, D.S. Yeung, X. Wang, The parameterization reduction of soft sets and its applications, Computer Mathematics Applications, 49(2005), 757-763.

P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Computers Mathematics Applications, 45(2003), 555-562.

Z. Kong, L. Gao, L. Wang and S. Li, The normal Parameter Reduction of Soft Sets and Its Algoritm, Computers and Mathematics with Applications, 56 (1) 3029-3037.

J. E. Macias Diaz, On modules which are isomorphic to relatively divisible or pure submodules of each other, Quaestiones Mathematicae, 38 (6), 2015.

J. Abuhlail, C. Lomp, Topological lattices and their applications to modules, Journal of Algebra Its Applications, 15 (3), (2015).

R. Ameri, R. Sadeghi, Gamma modules, Ratio Mathematica 20, 127{147 (2010).

A. H. Rezaei, B. Davvaz, Tensor product of gamma modules, Article in Afrika Mathematica, 26 (7), 1601- 1608, (2015).

Q-M. Sun, Z-L. Zhang and J.Liu, Soft sets and modules ( In Guoyin Wang, Tian-rui Li, Jerzy W. Grzymala-Busse, Duoqian Miao, Andrzej Skowron,Yiyu 54 Yao Eds.) Rough sets and knowledge technology, RSKT, Proceedings,Springer, 403-409, (2008).

D.Xiang, Soft module theory, IEEE, 2013, 10th International Conference on Fuzzy Systems and Knowledge Discovery.

T.Shah and S.Medhit, Primary decomposition in a soft ring and soft module, Iranian Journal of Science & Technology, 38A3 (Special issue-Mathematics) 311-320, (2014).

A.Erami, A.Hasankhani and A.B.Saeid, MV-modules in view of soft set theory, Çankaya University Journal of Science and Engineering, Volume 13, No. 1 (2016) 001{015.

M. I. Ali, F. Feng, X. Liu, W.K. Min, and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57 (9), 1547-1553, (2009).

D. Pei and D. Miao, From soft sets to information systems, In proceedings of Granular Computing (Eds: X. Hu., Q. Liu, A. Skowron, T.Y.Lin, R.R. Yager, B. Zhang) IEEE, 2, 617-621.

Z. Xiao, Y. Li, B. Zhong and X.Yang, Research on synthetically evaluating method for business competitive capacity based on soft set, Statical Research, 52-54.

H. Aktas, N. Cağman, Soft sets and soft groups, Inform. Sci. 177 (2007), 2726- 2735.

U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Computers and Mathematics with Applications, 59 (11), 2010, 3458- 3463.

Downloads

Published

2017-07-30

Issue

Vol. 32 (2017)

Section

Volume 32-2017

License

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:

  • Free access for all users worldwide
  • Increased visibility and readership
  • Rapid publication
  • No spatial constraints
  • Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)

Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. 
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.