Hohle平方根在Hoop代数上的应用
Application of Hohle's Square Roots on Hoop Algebras
AI总结：
本文在hoop代数上定义平方根，应用于滤子并证明商结构良态，引入好hoop代数类，探讨与布尔代数及Gödel代数关系，最终证明有界平方根hoop代数构成簇。
摘要：
平方根是研究（有序）代数结构性质的有用工具。在本文中，我们将利用这一工具来研究hoop代数。为此，我们定义了平方根，并首次尝试探讨该概念在此环境中的重要性性质。然后，鉴于平方根在获得新的hoop代数中的关键作用，我们将其应用于hoop代数的滤子，并表明在hoop代数关于其滤子的商结构上形成平方根是良态的。此外，引入了一类具有平方根的新的hoop代数，称为好hoop代数，并探讨了它与布尔代数和Gödel代数等其他有序代数类的关系。文中还提供了若干例子。最后，证明了所有具有平方根的有界hoop代数类构成一个簇。
英文摘要：
Square root is a useful tool to study the properties of (ordered) algebraic structures. In this article, we are going to employ this tool to study hoop algebras. To do so, we define square root and make the first attempt to explore the significance properties of this concept in this setting. Then, due to the key role of square roots in obtaining new hoop algebras, we apply them on the filters of hoop algebras, and show that the formation of square roots on quotient structures of hoop algebras by their filters is well-behaved. In addition, a new class of hoop algebras having square roots, so called good hoop algebras, is introduced and its relationships with other classes of ordered algebras such as Boolean algebras and Godel algebras are explored. Several examples are provided as well. Ultimately, it is shown that the class of all bounded hoop algebras with square roots is a variety.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
