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$2$-nil primary ideals of commutative semirings | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 فروردین 1405 اصل مقاله (196.74 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.31757.1855 | ||
| نویسندگان | ||
| M. Thakur1؛ T. R. Sharma* 2 | ||
| 1Srinivasa Ramanujan Department of Mathematics, Central University of Himachal Pradesh, Shahpur, India | ||
| 2Department of Mathematics, Himachal Pradesh University Regional Centre, Dharamshala | ||
| چکیده | ||
| In this paper, we extend the concept of primary ideals in commutative rings by introducing a new class, namely $2$-nil primary ideals, in a commutative semiring $S$ with $1 \neq 0$. We further investigate the structure of ideals by considering related classes such as $2$-nil ideals, $2$-absorbing ideals, and quasi-primary ideals. A comprehensive framework has been developed to emphasize the significance of $2$-nil primary ideals in semiring theory, focusing on their properties and interrelations. We provide arguments and illustrative examples that demonstrate how $2$-nil primary ideals are connected to several well-established classes of ideals, including prime ideals, primary ideals, $n$-ideals, $2$-absorbing ideals, and quasi-primary ideals. Finally, Theorem \ref{6} together with Corollaries \ref{q} and \ref{r} illustrates the applications of these ideals and highlights their significance within the theory of semirings. | ||
| کلیدواژهها | ||
| $n$-ideal؛ $2$-nil ideal؛ primary ideal؛ $2$-absorbing primary ideal | ||
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