EXPLORATION OF RING STRUCTURE FROM MULTISET CONTEXT
Abstract
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
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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.\\
Published
2025-12-04
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