پیوندهای مفید
آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 306 |
| تعداد مقالات | 2,645 |
| تعداد مشاهده مقاله | 3,966,370 |
| تعداد دریافت فایل اصل مقاله | 2,671,483 |
(σ, τ )-Derivation on ordered Γ-semihyperrings | ||
| Journal of Hyperstructures | ||
| دوره 12، شماره 2، اسفند 2023، صفحه 228-243 اصل مقاله (165.35 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2801 | ||
| نویسندگان | ||
| Lalita Nerkar* 1؛ Kishor Pawar2 | ||
| 1Kavayitri Bahinabai Chaudhari North Maharashtra University Jalgaon | ||
| 2Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon | ||
| چکیده | ||
| When a suitable partial ordered relation is attached to a Γ-semihyperring, it results into an ordered Γ-semihyperring. Concepts of an ordered Γ-semihyperring, Γ-band, idempotent Γ-semihyperring, totally or-dered Γ-semihyperring, positively ordered Γ-semihyperring, negatively or-dered Γ-semihyperring are introduced which are useful to study derivation on ordered Γ-semihyperrings. Derivation is nothing but an additive map-ping fulfilling the Leibniz rule. In this paper, we introduce the concept of (σ, τ)-derivation which is a generalization of σ-derivation and deriva-tion on Γ-semihyperring and study some properties of (σ, τ)-derivation on an ordered Γ-semihyperring. Some results reflecting different natures of (σ, τ)-derivation depending on natures of the endomorphisms are encoun-tere | ||
| کلیدواژه‌ها | ||
| Γ-semihyperring؛ ordered Γ-semihyperring؛ (σ؛ τ)-derivation | ||
| مراجع | ||
|
[1] L. K. Ardekani and B. Davvaz, Derivations of Γ-(semi)hyperrings, Ukrainian Math J, 70 (2018), 1165-1175. [2] M. Ashraf, A. Khan and C. Haetinger, On (σ, τ)-higher derivations in prime rings, Int.Electron. J. Algebra 8 (2010), 65-79. [3] A. Asokkumar, Derivation in hyperrings and prime hyperrings, Iranian Journal of Math-ematical Sciences and Informatics, 8(1) (2013), 1–13. [4] J. Chvalina, Commutative hypergroups in the sence of Marty and ordered sets, Proc. In-ternat. Conf. Olomouck (Czech Rep.), (1994), 19–30. [5] J. Chvalina and J. Moucka, Hypergroups determined by orderings with regular endomor-phism monoids, Ital. J. Pure Appl. Math., 16 (2004), 227–242. [6] P. Corsini and V. Leoreanu-Fotea, Applications of Hyperstructure Theory, Advances In Mathematics, Dordrecht: Kluwer Academic Publishers, (2003). [7] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, Internat. Aca-demic Press, USA, (2007). [8] S. O. Dehkordi and B. Davvaz, Ideal theory in Γ-semihyperrings, Iran. J. Sci. Technol.Trans. A. Sci., 37(3) (2013), 251-263. [9] . Golbasi and E. Koc, Some commutativity theorems of prime rings with generalized (σ, τ)-derivation, Commun. Korean Math. Soc. 26(3) (2011), 445-454. [10] D. Heidari and B. Davvaz, On ordered hyperstructures, Politehn. Univ. Bucharest Sci.Bull. Ser. A Appl. Math. Phys., 73(2) (2011), 85–96. [11] S. Hoskova, Representation of quasi-order hypergroups, Glob. J. Pure Appl. Math.,1(2005), 173–176. [12] S. Hoskova, Upper order hypergroups as a reective subcategory of subquasiorder hyper-groups, Ital. J. Pure Appl. Math., 20 (2006), 215–222. [13] A. Iampan, Characterizing ordered Bi-Ideals in ordered Γ-semigroups, Iranian Journal of Mathematical Sciences and Informatics, 4(1) (2009), 17–25. [14] F. J. Jing, On derivations of Γ-rings, J. Qufu Norm. Univ., Nat. Sci., 13 (1987), 159-161. [15] K. Kaya, On a (σ, τ)-derivations of prime rings, Doga Tr. J. Math. D.C. 12 s 2 (1988),46–51. [16] F. Marty, Sur une generalization de la notion de group, In Proc. of the Eighth Congress Math. Scandinaves, Stockholm, Sweden, (1934), 45-49. [17] L. P. Nerkar and K. F. Pawar, Some results on derivations on Γ-(semi)hyperrings, pre-print communicated. [18] L. P. Nerkar and K. F. Pawar, ?-derivations on Γ-semihyperrings, pre-print communicated. [19] J. J. Patil and K. F. Pawar, On quasi-ideals on Γ-semihyperrings, Journal of Hyperstruc-tures 8 (2) (2019), 123-134. [20] J. Patil and K. Pawar, On uniformly strongly prime Γ-semihyperring, Kragujevac Journal of Mathematics, 48(1) (2024), 79–87. [21] K. F. Pawar, J. J. Patil and B. Davazz, On a regular Γ-semihyperrings and idempotent Γ-semihyperrings, Kyungpook Math. J., 59 (2019), 35-45. [22] E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100. [23] D. Qing, Derivations in prime rings, Rend. Circ. Mat. Palermo (2) 42(1) (1993), 21–28. [24] M. M. K. Rao, B. Venkateshwarlu, B. R. Kumar and K. R. Kumar, (f,g) derivation of ordered-semirings, Mathematica Moravica, 22(1) (2018), 107–121. | ||
|
آمار تعداد مشاهده مقاله: 47 تعداد دریافت فایل اصل مقاله: 44 |
||