A proper ideal I of a commutative ring R is called lifting whenever idempotents of R/I lift to idempotents of R. In this paper, many of the basic properties of lifting ideals are studied and we prove and extend some well-known results concerning lifting ideals and lifting idempotents by a new approach. Furthermore, we give a necessary and sufficient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal lifting ideals.

中文翻译：

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提升理想的共极大因式分解

适当的理想一世交换环的R每当幂等时称为提升R/一世提升到幂等R. 本文研究了提升理想的许多基本性质，并通过一种新的方法证明和扩展了一些关于提升理想和提升幂等性的著名结果。此外，我们给出了一个交换环的每一个真理想是成对共极大提升理想的乘积的充要条件。