This paper deals with minimal reductions and core of ideals in various settings of pullback constructions with the aim of building original examples, where we explicitly compute the core. To this purpose, we use techniques and objects from multiplicative ideal theory to investigate the existence of minimal reductions in Section 2 and then develop explicit formulas for the core in Section 3. The last section features illustrative examples and counterexamples.

中文翻译：

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最小的减少和回调的理想核心

本文以构建原始示例为目标，探讨了在回调构造的各种设置中的最小化还原和理想的核心，我们在其中明确地计算了核心。为此，我们使用乘法理想理论中的技术和对象来研究第2节中最小化约简的存在，然后在第3节中为核心创建明确的公式。最后一节以说明性示例和反例为特色。