EXPLORATION OF RING STRUCTURE FROM MULTISET CONTEXT
DOI:
https://doi.org/10.5269/bspm.66355Abstract
The prime intent of this research paper is to build up the perception of ring structure in multiset framework and explore some of their crucial properties
References
\noindent $[1]$ J. A. Awolola and A. M. Ibrahim, {\it Some results on multigroups}, Quasigroups and Related Systems, {\bf 24},(2016), 169–177.\\
\noindent $[2]$ V.Cerf, E.Fernandez, K.Gostelow and S.Volausky, {\it Formal control and low properties of a model of computation, Report ENG 7178}, Computer Science Department, University of California, Los Angeles,CA, December, (1971), pp. 81.\\
\noindent $[3]$ P.A. Ejegwa, {\it Upper and Lower Cuts of Multigroups, Prajna}, International Journal of Mathematical Sciences and Applications,{\bf 1}, (2017), 19–26.\\
\noindent $[4]$ K. P. Girish and S.J. John, {\it Relations and functions in multiset context}, Information sciences, {\bf 179}, (2009), 758–768.\\
\noindent $[5]$ K. P. Girish and S.J. John, {\it Rough Multiset and its Multiset Topology}, Lecture Notes in Computer Science, Springer. Berlin, Heidelberg, 6600, (2011), 62–80.\\
\noindent $[6]$ K. P. Girish and S.J. John, {\it On multiset topologies}, Theory Appl. Math. Comput. Sci., {\bf 2}, (2012), 37–52.\\
\noindent$[7]$ K. P. Girish and S.J. John, {\it Multiset topologies induced by multiset relations}, Inf. Sci., {\bf 188},(2012), 298–313.\\
\noindent$[8]$ A.M. Ibrahim and D. Singh, {\it An Outline of Multiset Space Algebra}, International Journal of Algebra, {\bf 5(31)}, (2011), 1515 – 1525.\\
\noindent$[9]$ A.M. Ibrahim and P.A. Ejegwa, {\it A Survey on the Concept of Multigroups}, Journal of the Nigerian Association of Mathematical Physics,{\bf 38},(2016), 1–8.\\
\noindent$[10]$ R. Kellil, {\it Sum and product of Fuzzy Ideals of a ring}, International Journal of Mathematics and Computer Science., {\bf 13},(2018), 187–205.\\
\noindent$[11]$ D. E. Knuth, {\it The Art of Computer Programming}, Semi numerical Algorithms, Adison- Wesley, {\bf 2}, (1981).\\
\noindent$[12]$ S. K. Nazmul , P.M Ajumdar and S.K.Samanta, {\it On Multisets and Multigroups}, Annals of Fuzzy Mathematics and Informatics, {\bf 3}, (2013), 643–656.\\
\noindent$[13]$ A. Rosenfeld, {\it Fuzzy Groups}, Journal of Mathematical Analysis and Applications, {\bf 35},(1971), 512–517.\\
\noindent$[14]$ S. Sebastian, M Ercy K. Jacob, V. M. M Ary and D. M. Daise, {\it On Fuzzy Ideals and Rings}, Journal of Computer and Mathematical Sciences, {\bf 3(1)},(2012), 115–120.\\
\noindent$[15]$ P. Suma and S. J. John , Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures, IGI Global., {\it Chapter5,Multiset Approach to Algebraic Structures},(2019) 78–90.\\
\noindent$[16]$ P. Suma and S.J. John, {\it Exploration of Multiset Ideals}, AIP Conference Proceedings {\bf 2336}, (2021), 05-12. https://doi.org/10.1063/5.0045816\\
\noindent$[17]$ U. M. Swamy and K. L. N. Swamy, {\it Fuzzy Prime Ideals Of Rings}, Journal of Mathematical Analysis and Applications, {\bf 134}, (1988), 94–103.\\
\noindent$[18]$ Y. Tella and S. Daniel, {\it A Study of Group Theory in the Context of Multiset Theory}, International Journal of Science and Technology, {\bf 2(8)},(2013), 609–615.\\
\noindent$[19]$ B. C. Tripathy, S.Debnath and D.Rakshit, {\it On multiset group}, Proyecciones Journal of Mathematics, {\bf 33}, (2018), 479–489.\\
\noindent$[20]$ Y. Li, X. Wang, and L. Yang, {\it A Study of $\lambda,\mu$ -Fuzzy Subgroups}, Journal of Applied Mathematics. (2013). http://dx.doi.org/10.1155/2013/485768.\\
\noindent $[2]$ V.Cerf, E.Fernandez, K.Gostelow and S.Volausky, {\it Formal control and low properties of a model of computation, Report ENG 7178}, Computer Science Department, University of California, Los Angeles,CA, December, (1971), pp. 81.\\
\noindent $[3]$ P.A. Ejegwa, {\it Upper and Lower Cuts of Multigroups, Prajna}, International Journal of Mathematical Sciences and Applications,{\bf 1}, (2017), 19–26.\\
\noindent $[4]$ K. P. Girish and S.J. John, {\it Relations and functions in multiset context}, Information sciences, {\bf 179}, (2009), 758–768.\\
\noindent $[5]$ K. P. Girish and S.J. John, {\it Rough Multiset and its Multiset Topology}, Lecture Notes in Computer Science, Springer. Berlin, Heidelberg, 6600, (2011), 62–80.\\
\noindent $[6]$ K. P. Girish and S.J. John, {\it On multiset topologies}, Theory Appl. Math. Comput. Sci., {\bf 2}, (2012), 37–52.\\
\noindent$[7]$ K. P. Girish and S.J. John, {\it Multiset topologies induced by multiset relations}, Inf. Sci., {\bf 188},(2012), 298–313.\\
\noindent$[8]$ A.M. Ibrahim and D. Singh, {\it An Outline of Multiset Space Algebra}, International Journal of Algebra, {\bf 5(31)}, (2011), 1515 – 1525.\\
\noindent$[9]$ A.M. Ibrahim and P.A. Ejegwa, {\it A Survey on the Concept of Multigroups}, Journal of the Nigerian Association of Mathematical Physics,{\bf 38},(2016), 1–8.\\
\noindent$[10]$ R. Kellil, {\it Sum and product of Fuzzy Ideals of a ring}, International Journal of Mathematics and Computer Science., {\bf 13},(2018), 187–205.\\
\noindent$[11]$ D. E. Knuth, {\it The Art of Computer Programming}, Semi numerical Algorithms, Adison- Wesley, {\bf 2}, (1981).\\
\noindent$[12]$ S. K. Nazmul , P.M Ajumdar and S.K.Samanta, {\it On Multisets and Multigroups}, Annals of Fuzzy Mathematics and Informatics, {\bf 3}, (2013), 643–656.\\
\noindent$[13]$ A. Rosenfeld, {\it Fuzzy Groups}, Journal of Mathematical Analysis and Applications, {\bf 35},(1971), 512–517.\\
\noindent$[14]$ S. Sebastian, M Ercy K. Jacob, V. M. M Ary and D. M. Daise, {\it On Fuzzy Ideals and Rings}, Journal of Computer and Mathematical Sciences, {\bf 3(1)},(2012), 115–120.\\
\noindent$[15]$ P. Suma and S. J. John , Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures, IGI Global., {\it Chapter5,Multiset Approach to Algebraic Structures},(2019) 78–90.\\
\noindent$[16]$ P. Suma and S.J. John, {\it Exploration of Multiset Ideals}, AIP Conference Proceedings {\bf 2336}, (2021), 05-12. https://doi.org/10.1063/5.0045816\\
\noindent$[17]$ U. M. Swamy and K. L. N. Swamy, {\it Fuzzy Prime Ideals Of Rings}, Journal of Mathematical Analysis and Applications, {\bf 134}, (1988), 94–103.\\
\noindent$[18]$ Y. Tella and S. Daniel, {\it A Study of Group Theory in the Context of Multiset Theory}, International Journal of Science and Technology, {\bf 2(8)},(2013), 609–615.\\
\noindent$[19]$ B. C. Tripathy, S.Debnath and D.Rakshit, {\it On multiset group}, Proyecciones Journal of Mathematics, {\bf 33}, (2018), 479–489.\\
\noindent$[20]$ Y. Li, X. Wang, and L. Yang, {\it A Study of $\lambda,\mu$ -Fuzzy Subgroups}, Journal of Applied Mathematics. (2013). http://dx.doi.org/10.1155/2013/485768.\\
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2025-12-04
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