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Regular equivalence and strongly regular equivalence on multiplicative ternary hyperring | ||
| Journal of Hyperstructures | ||
| دوره 4، شماره 1، شهریور 2015، صفحه 20-36 اصل مقاله (113.87 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2015.2595 | ||
| نویسندگان | ||
| Md Salim Masud Molla* 1؛ T. Chanda2؛ T. K. Dutta3 | ||
| 1Department of Mathematics, Darjeeling Government College, P.O.Box 734101, Darjeeling, India | ||
| 2Department of Mathematics, Ananda Mohan College, P.O.Box 700009, Kolkata, India | ||
| 3Department of Pure Mathematics, University of Calcutta, P.O.Box 700019, Kolkata, India | ||
| چکیده | ||
| We introduce the notion of a multiplicative ternary hyperring, consider regular equivalences and strongly regular equivalences of a multiplicative ternary hyperring and investigate their properties. As a consequence, three isomorphism theorems on multiplicative ternary hyperrings are obtained. | ||
| کلیدواژهها | ||
| Binary relation؛ equivalence relation؛ regular and strongly regular equivalence relation؛ ternary hyperrings | ||
| مراجع | ||
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[1] A. Assokumar and M. Velrajan, Hyperring of Matrices over a regular Hyperring., Italian Journal of Pure and Applied Mathematics,23 No.23( 2008) [2] B. Davvaz, Isomorphism Theorems of Hyperrings. Indian Journal of Pure and Applied Mathematics.35 No.3(2004) [3] B. Davvaz and S. Mirvakili, Relations on Krasner (m, n)- hyperrings. European Journal of Combinatories. 31 (2010), http: //dx.doi.org/10.1016/j.ejc.2009.07.006. [4] B. Davvaz and V. Leoreanu-Fotea Hyperring Theory and Applications, Interna-tional Academic press, Palm Harbor. Florida, USA(2007). [5] D. H. Lehmer, A Ternary Analogue of Abelian Groups, Amer. J. Math., 54(2) (1932), 329-338. [6] E. L. Post, Polyadic Groups, Trans. Amer. Math. Soc., 18 (1940) 208-350. [7] F. Marty, Sur une generalization de la notion de group, 8th congress des Math. Scandenaves stockholm, (1934), 45-49. [8] H. Pr¨ufer, Theorie der Abelschen Gruppen, I. Grundeigenschaften, Math. Z., 20 (1924), 165-187. [9] J. R. Castillo and Jocelyn S. Paradero-Vilela, Quotient and Homomorphism in Ternary Hyperrings, International Journal of Mathematical Analysis, 8 (2014).no.58, 2845-2859. [10] M. De Salvo. Hyperring and Hyperfields. Anneles Scientifiques de Universite de Clermont-Ferrand II No. 22,(1984). [11] M. Krasner, A Class of hyperrings and hyperfields, Internat. J. Math, Sci., 6 (1983) 307-311. [12] R. Rota, R, Strongly Distribute Multiplicative Hyperrings. Journal of Geometry. 39, No-1(1990) 130-138 [13] S. M. Anvariyeh and S. Mirvakili, Canonical (m, n)-Hypermodules over krasner (m, n)-ary Hyperrings, Iranian Journal of Mathematical Science and Informatics, 7 No 2(2012), [14] W. G. Lister, Ternary Rings, Trans. Amer. Math. Soc., 154 (1971), 37-55. | ||
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