In this paper, we introduce a class of commutative rings which is a generalization of $\mathrm{\text{ZD}}$-rings and rings with Noetherian spectrum. A ring $R$ is called strongly$J$-Noetherian whenever the ring $R_r$ is $J$-Noetherian for every non-nilpotent $r\in R$. We give some characterizations for strongly $J$-Noetherian rings and, among the other results, we show that if $R[[x]]$ is strongly $J$-Noetherian, then $R$ has Noetherian spectrum, which is a generalization of Theorem 2 in Gilmer and Heinzer [The Laskerian property, power series rings, and Noetherian spectra, Proc. Amer. Math. Soc.79 (1980) 13–16].

在本文中，我们介绍了一类交换环，它是$\mathrm{\text{ZD}}$- 环和具有诺特谱的环。戒指$R$被强烈称为$Ĵ$-Noetherian每当戒指$R_r$是$Ĵ$-Noetherian 为每一个非幂零者$r\in R$. 我们给出了一些强烈的特征$Ĵ$-Noetherian 环，除其他结果外，我们证明如果$R[[X]]$是强烈的$Ĵ$-Noetherian，然后$R$有 Noetherian 谱，这是 Gilmer 和 Heinzer [The Laskerian property, power series ring, and Noetherian spectrum, Proc. 中的定理 2 的推广。阿米尔。数学。社会党。79 (1980) 13-16]。