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A Zariski-like topology on the 2-prime spectrum of commutative rings | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 2، اسفند 2025، صفحه 75-84 اصل مقاله (161.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.26914.1640 | ||
| نویسندگان | ||
| H. Roshan Shekalgourabi* ؛ D. Hassanzadeh Lelekaami | ||
| Department of Basic Sciences, Arak University of Technology, Arak, Iran | ||
| چکیده | ||
| A proper ideal $P$ of a ring $R$ is called \emph{2-prime} if for all $x, y \in R$ such that $xy\in P$, then either $x^2 \in P$ or $y^2 \in P$. In this paper, we introduce a Zariski topology on the set of all 2-prime ideals of commutative rings. We investigate this topology and clarify the interplay between the properties of this topological space and the algebraic properties of the ring under consideration. | ||
| کلیدواژهها | ||
| 2-prime ideal؛ 2-Zariski topology؛ Radical | ||
| مراجع | ||
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