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On quasi-hyperideals and bi-hyperideals in multiplicative hypersemirings | ||
| Journal of Hyperstructures | ||
| دوره 11، شماره 2، اسفند 2022، صفحه 196-213 اصل مقاله (311.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2563 | ||
| نویسنده | ||
| Md Salim Masud Molla* | ||
| Department of Mathematics, Darjeeling Government College, P.O.Box 734101, Darjeeling, India | ||
| چکیده | ||
| In this paper we introduce the notion of quasi-hyperideal in multiplicative hypersemirings which is a generalization of one-sided hyperideal and study some of its properties and obtain some characterizations of quasi-hyperideal in multiplicative hypersemirings. Also, we introduce the notion of bi-hyperideal in multiplicative hypersemirings. We prove that in a multiplicative hypersemiring every quasi-hyperideal is a bi-hyperideal, but the converse is not true. Lastly, we characterize regular multiplicative hypersemiring with the help of quasi-hyperideal and bi-hyperideal. | ||
| کلیدواژه‌ها | ||
| Multiplicative hypersemiring؛ minimal left hyperideal؛ minimal right hyperideal؛ quasi-hyperideal؛ bi-hyperideal؛ regular multiplicative hypersemiring | ||
| مراجع | ||
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[1] A. M. Ibrahim and P. A. Ejegwa, A survey on the concept of multigroup, Journal of the Nigerian Association of Mathematical Physics. 38 (2016), 1-8. [2] B. Davvaz and V. L. Fotea, Hyperring Theory and Applications, International Academic Press. Palm Harbor, Florida, USA. (2007). [3] C. Donges, On Quasi-ideals of semirings, Int. J. Math and Math. Sci. 17(1) (1994), 47-58. [4] E. S. Sevim, B. A. Ersoy and B. Davvaz, Primary hyperideals of multiplicative hyperrings, Eurasian Bulletin of Mathematics, 1(1) (2018). [5] F. Marty, Sur une generalization de la notion de group, 8th congress des Math. Scandenaves stockholm, 45-49, (1934). [6] F. M. Sioson, Ideal theory in ternary semigroups, Math. Japonica. 10 (1965), 63-84. [7] H. Bordbar and I. Cristea, Height of prime hyperideals in Krasner hyperrings, Filomat, 31(19), 6153-6163. DOI:10.2298/FIL1719153B. [8] H. Bordbar, I. Cristea and M. Novak, Height of Hyperideals in Noetherian Krasner Hyperrings, University Politehnica of Bucharest Scienti c Bulletin-Series AApplied Mathematics and Physics, 79(2) (2017), 31-42. [9] K. Hila, B. Davvaz and K. Naka, On quasi-hyperideals in semihypergroups, Communication in Algebra. 39 (2011), 4183 4194. DOI: 10.1080/00927872.2010.521932. [10] M. Dresher and O. Ore, Theory of multigroup, Amer. J. of Mathematics, 60(3) (1938), 705-733. [11] M. Hamidi, R. Ameri and A. A. Tavakoli, Boolean Rings Based on Multirings, J. Sci .I. R. I., 32(2) (2011), 159168. [12] M. Hamidi, R. Ameri and A. A. Tavakoli, Valued-potent (general) multirings, J. alg. sys, 10(1) (2022), 49-68. [13] M. Krasner, A class of hyperrings and hyperfields, International J. Math and Math Sci. 6(2) (1983), 307-312. [14] M. Marshall, Real reduced multirings and multifields, J. Pure Appl. Algebra. 205 (2006), 452-468. [15] Md Salim, T. Chanda and T. K. Dutta, Regular equivalence and strongly regular equivalence on multiplicative ternary hyperring, Journal of Hyperstructures. 4(1) (2015), 20-36. [16] N. Tamang and M. Mandal, Hyperideals of a Ternary Hypersemiring, Bull. Cal. Math. Soc., 110(5) (2018), 385-398. [17] O. Steinfeld, Uber die Quasiideale Halbgruppen, Publ. Math. Debrecen. 4 (1956), 262-275. [18] P. Corsini, Hypergraphs and hypergroups, Algebra Universalis, 35(1996), 548-555. [19] P. Corsini, Hypergroups reguliers et hypermodules, Ann. Univ. Ferrara-Sez., VIISc. Mat, 20 (1975), 121-235. [20] P. Corsini, Sur les semihypergroupes, Atti Soc. Pelor., Sc. Mat. Fis. Nat, XXVI, (1980). [21] P. Corsini and V. L. Fotea, Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic, Dodrecht, The Netherlands, (2003). [22] R. Ameri, A. Kordi and S. Sarka-Mayerova, Multiplicative hyperring of fractions and coprime hyperideals, An. Stiint. Univ. Ovidius Constanta Ser. Mat, 25(1)(2017), 5-23. DOI: 10.1515/auom-2017-0001. | ||
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