In the present paper, we introduce the notions of quasi-Boolean algebras as the generalization of Boolean algebras. First we discuss the related properties of quasi-Boolean algebras. Second we define filters of quasi-Boolean algebras and investigate some properties of filters in quasi-Boolean algebras. We also show that there is a one-to-one correspondence between the set of filters and the set of filter congruences on a quasi-Boolean algebra. Then we investigate the prime filters and maximal filters of quasi-Boolean algebras, showing that the prime filters of a quasi-Boolean algebra are precisely the maximal filters and the prime spectrum of a quasi-Boolean algebra is a compact Hausdorff topological space. Finally, we define and study the reticulation of a quasi-Boolean algebra.

中文翻译：

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准布尔代数谱

在本文中，我们介绍了准布尔代数的概念作为布尔代数的推广。首先我们讨论准布尔代数的相关性质。其次，我们定义了准布尔代数的滤波器，并研究了准布尔代数中滤波器的一些性质。我们还表明，在准布尔代数上，滤波器集和滤波器同余集之间存在一一对应关系。然后我们研究了拟布尔代数的素滤子和极大滤子，表明准布尔代数的素滤子恰好是极大滤子，而拟布尔代数的素谱是紧Hausdorff拓扑空间。最后，我们定义并研究了一个准布尔代数的网状化。