Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, the notion of $S$-pseudo-irreducible ideals of $R$ as a generalization of pseudo-irreducible ideals is introduced and some related properties are investigated. Then, we consider the decomposition of proper ideals of a ring into a product of pairwise comaximal $S$-pseudo-irreducible ideals. Some other results are obtained too.

中文翻译：

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S-伪不可约理想

让$R$是一个具有恒等式的交换环并且$\mathrm{小号}$的乘法子集$R$. 在本文中，概念$\mathrm{小号}$——伪不可约理想$R$作为伪不可约理想的推广，并研究了一些相关性质。然后，我们考虑将环的真理想分解为成对共极大的乘积$\mathrm{小号}$- 伪不可约理想。也得到了一些其他的结果。