Abstract In this paper, by using the ideal theory in residuated lattices, we construct the prime and maximal spectra (Zariski topology), proving that the prime and maximal spectra are compact topological spaces, and in the case of De Morgan residuated lattices they become compact T 0 {T}_{0} topological spaces. At the same time, we define and study the reticulation functor between De Morgan residuated lattices and bounded distributive lattices. Moreover, we study the I-topology (I comes from ideal) and the stable topology and we define the concept of pure ideal. We conclude that the I-topology is in fact the restriction of Zariski topology to the lattice of ideals, but we use it for simplicity. Finally, based on pure ideals, we define the normal De Morgan residuated lattice (L is normal iff every proper ideal of L is a pure ideal) and we offer some characterizations.

中文翻译：

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素数和极大谱以及剩余点阵的网状化以及在 De Morgan 剩余点阵中的应用

摘要 本文利用剩余格的理想理论，构造了质数和极大谱（Zariski 拓扑），证明质数和极大谱是紧拓扑空间，在 De Morgan 剩余格的情况下，它们变得紧致T 0 {T}_{0} 拓扑空间。同时，定义并研究了De Morgan剩余格与有界分配格之间的网状函子。此外，我们研究了I-拓扑（I来自理想）和稳定拓扑，并定义了纯理想的概念。我们得出结论，I-拓扑实际上是 Zariski 拓扑对理想格的限制，但为了简单起见，我们使用它。最后，基于纯粹的理想，