希尔伯特代数和布劳威尔半格簇中自由代数的一般构造
A generic construction of free algebras in varieties of Hilbert algebras and Brouwerian semilattices
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中文总结 AI 辅助
本文用统一方法构造\(n\)生成自由希尔伯特代数和布劳威尔半格，适用于能描述次直不可约代数的簇，稍作修改可得含零簇的构造，还给出示例及关于含零希尔伯特代数簇结构完备性的结果。
中文摘要 AI 辅助
我们给出了一种通过统一方法构造\(n\)生成自由希尔伯特代数和布劳威尔半格的方法，该方法适用于任何希尔伯特代数或布劳威尔半格簇，只要能对该簇中次直不可约代数进行可控描述。稍作修改可得到含零的希尔伯特代数和布劳威尔半格簇的类似构造。作为示例，构造了有界高度和有界宽度簇中的自由代数，还得到了线性希尔伯特代数自由谱的闭式。最后得到了一些关于含零希尔伯特代数簇结构完备性的结果。
英文摘要
We give a generic construction of the n-generated free Hilbert algebras and Brouwerian semilattices by a uniform method applicable to any variety of Hilbert algebras or Brouwerian semilattices, as long as a manageable description of subdirectly irreducible algebras in that variety is available. A slight modification yields analogous constructions for varieties of Hilbert algebras and Brouwerian semilattices with zero. As examples we construct free algebras in varieties of bounded height and of bounded width; we also find a closed formula for the free spectrum of linear Hilbert algebras. Finally, we obtain a few results on structural completeness of varieties of Hilbert algebras with zero, in particular, we give a sufficient condition for a quasi-equation to be equivalent to an equation.
