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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2023.1
- 수록면
- 1 - 9 (9page)
- DOI
- 10.4134/CKMS.c210057
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초록· 키워드
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An le-module $M$ over a commutative ring $R$ is a complete lattice ordered additive monoid $(M, \leqslant, +)$ having the greatest element $e$ together with a module like action of $R$. This article characterizes the le-modules $_RM$ such that the pseudo-prime spectrum $X_M$ endowed with the Zariski topology is a Noetherian topological space. If the ring $R$ is Noetherian and the pseudo-prime radical of every submodule elements of $_{R}M$ coincides with its Zariski radical, then $X_{M}$ is a Noetherian topological space. Also we prove that if $R$ is Noetherian and for every submodule element $n$ of $M$ there is an ideal $I$ of $R$ such that $V(n) = V(Ie)$, then the topological space $X_{M}$ is spectral.
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