交换半环中的拟S-n-理想
Quasi S-n-ideals in commutative semirings
- Jadavpur University（贾达普大学）
- Kanyashree University（卡纳什里大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在带单位元的交换半环中引入拟S-n-理想概念，研究其与相关理想的关系、局部化性态及商多项式半环中的情况，还探讨其通过理想化与融合构造的自然扩张。
AI中文摘要：
设R为带单位元（1≠0）的交换半环，S为R的真乘法闭子集。本文在交换半环中引入拟S-n-理想的概念，研究其基本性质，建立它与拟n-理想、S-n-理想、S-素理想、S-准素理想的关系，探讨其在局部化下的性态，最后确定商多项式半环R[x]/⟨x^m⟩中的拟S-n-理想，并通过理想化与融合构造研究其自然扩张。
英文摘要：
Let $R$ be a commutative semiring with unity $(1\neq0)$, and let $S$ be a proper multiplicatively closed subset of $R$. In this paper, we introduce the notion of quasi $S$-$n$-ideals in commutative semirings. We the study basic property of quasi $S$-$n$-ideals and establish their relationships with quasi $n$-ideals, $S$-$n$-ideals, $S$-prime ideals, and $S$-primary ideals. We also investigate their behavior under localization. Finally, we determine quasi $S$-$n$-ideals in the quotient polynomial semiring $R[x]/\langle x^m\rangle$ and study their natural extensions via the constructions of idealization and amalgamation.
