In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties under homomorphic image and their transfer to various contexts of constructions such as direct product, trivial ring extension and amalgamated duplication of a ring along an ideal. Our results generate examples that enrich the current literature with new and original families of rings satisfying these properties.

中文翻译：

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具有可逆根因式分解的交换环

在本文中，我们研究了环的类别，其中每个真（常规）理想都可以分解为可逆理想乘以真激进理想的非空乘积。更准确地说，我们研究了这些属性在同态图像下的稳定性以及它们转移到各种构造上下文中，例如直接乘积、平凡的环扩展和沿着理想的环的合并复制。我们的结果生成了一些示例，这些示例通过满足这些属性的新的和原始的环族来丰富当前的文献。