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Some results on 1-absorbing prime ideals of commutative semirings | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 16 فروردین 1405 اصل مقاله (204.92 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.29872.1772 | ||
| نویسنده | ||
| H. K. Ranote* | ||
| Department of Mathematics, Maharaja Agarsen University, (Baddi) Solan, India | ||
| چکیده | ||
| The main objective of this paper is to study the concept of 1-absorbing prime ideals in commutative semirings as a generalization of 1-absorbing prime ideals in commutative rings. We examine several characterizations and examples of 1-absorbing prime ideals and also investigate the 1-absorbing Prime Avoidance Theorem for such ideals. Moreover, we study the concept of 1-absorbing primary ideals in commutative semirings and studying a method for constructing 1-absorbing primary ideals that are not necessarily primary ideals. Finally, we examine various characterizations and examples of 1-absorbing primary ideals in commutative semirings. | ||
| کلیدواژهها | ||
| 1-absorbing prime ideals؛ 1-absorbing primary ideals؛ Semirings | ||
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