In this paper, we introduce and study the concept of strongly dccr${}^{\star }$ modules. Strongly dccr${}^{\star }$ condition generalizes the class of Artinian modules and it is stronger than dccr${}^{\star }$ condition. Let $R$ be a commutative ring with nonzero identity and $M$ a unital $R$-module. A module $M$ is said to be strongly $dcc{r}^{\star }$ if for every submodule $N$ of $M$ and every sequence of elements $(a_i)$ of $R$, the descending chain of submodules $a_{1}N\supseteq a_1{a}_{2}N\supseteq \cdots \supseteq a_1{a}_2\dots a_{n}N\supseteq \cdots$ of $M$ is stationary. We give many examples and properties of strongly dccr${}^{\star }$. Moreover, we characterize strongly dccr${}^{\star }$ in terms of some known class of rings and modules, for instance in perfect rings, strongly special modules and principally cogenerately modules. Finally, we give a version of Union Theorem and Nakayama’s Lemma in light of strongly dccr${}^{\star }$ concept.

在本文中，我们介绍并研究了强 dccr 的概念。${}^{\star }$模块。强烈dccr${}^{\star }$condition 泛化了 Artinian 模块的类，它比 dccr 更强${}^{\star }$健康）状况。让$R$是一个具有非零恒等式的交换环，并且$米$一个单位$R$-模块。一个模块$米$据说强烈$dCC{r}^{\star }$如果对于每个子模块$ñ$的$米$以及每一个元素序列$({\mathrm{一个}}_{\mathrm{一世}})$的$R$, 子模块的降链${\mathrm{一个}}_1ñ\supseteq {\mathrm{一个}}_1{\mathrm{一个}}_2ñ\supseteq \cdots \supseteq {\mathrm{一个}}_1{\mathrm{一个}}_2\dots {\mathrm{一个}}_nñ\supseteq \cdots$的$米$是静止的。我们给出了很多强 dccr 的例子和性质${}^{\star }$. 此外，我们强烈表征 dccr${}^{\star }$就某些已知的环和模类而言，例如在完美环中，强特殊模和主要是共生模。最后，我们根据强 dccr 给出联合定理和中山引理的一个版本${}^{\star }$概念。