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Some results on $2$-absorbing $ R_{\Gamma}-$semimodules over $ \Gamma-$semirings | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 2، اسفند 2025، صفحه 187-198 اصل مقاله (165.95 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.26633.1627 | ||
| نویسنده | ||
| H. K. Ranote* | ||
| Department of Mathematics, Maharaja Agarsen University, (Baddi) Solan, India | ||
| چکیده | ||
| The purpose of this paper is to introduce the notion of 2-absorbing $ R_{\Gamma}-$semimodules over $ \Gamma-$semirings, as a generalization of 2-absorbing semimodules over semirings and study various results related to them. | ||
| کلیدواژهها | ||
| $k$-ideal؛ $ R_{\Gamma}-$semimodule؛ Strong $ R_{\Gamma}-$semimodule؛ $2$-absorbing $ R_{\Gamma}-$semimodule؛ $ \Gamma -$ semiring | ||
| مراجع | ||
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[1] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75 (2007), 417-429. [2] A. Y. Darani, On 2-absorbing and weakly 2-absorbing ideals of commutative semirings, Kyungpook Math. J., 52 (2012), 91-97. [3] M. K. Dubey and P. Sarohe, On 2-absorbing semimodules, Quasigroups and Related Systems, 21 (2013), 175-184. [4] T. K. Dutta and S. K. Sardar, On prime ideals and prime radicals of Γ− semirings, An. Stiint. Univ. Al. I. Cuza Iasi Mat., 46 (2001), 319-329. [5] T. K. Dutta and U. Dasgupta, Properties of Γ− S-semimodules via its associated semimodules, Southeast Asian Bulletin of Mathematics, 28 (2004), 243-250 [6] W. M. Fakieh and F. A. Alhawiti, Ideal theory in commutative Γ− semirings, International Journal of Algebra, (2) 15 (2021), 77-101. [7] S. M. A. Galindo and G. C. Petalcorin, Some properties of Γ− semimodules over Γ− semirings, Journal of Algebra and Applied Mathematics, (2) 13 (2015), 97-113. [8] S. M. A. Galindo and G. C. Petalcorin, Partitioning and substractive SΓ− semimodules, Journal of Algebra and Applied Mathematics, (1) 14 (2016), 59-78. [9] H. K. Ranote, On some properties of 2-absorbing ideals in commutative Γ− semirings, Bulletin of the Institute of Mathematics., (communicated) [10] M. M. K. Rao, Γ− semirings-I, South East Asian Bull. of Math., 19 (1995), 49-54. [11] N. Sangjaer and S. Pianskool, On 2-absorbing primary ideals in commutative Γ− semirings, Thai Journal of Mathematics, (2019), 49-60. [12] S. K. Sardar and U. Dasgupta, On primitive Γ− semiring, Novi Sad J. Math., (1) 34 (2004), 1-12. [13] T. R. Sharma and S. Gupta, Some conditions on Γ− semirings, Journal of Combinatorics Information and System Sciences, 41 (2016), 79-87. | ||
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