Application of Höhle’s square roots on Hoop algebras

Motamedi Nezhad, Mohammad Mahdi; Madanshekaf, Ali

doi:10.22103/jmmr.2026.26238.1897

Application of Höhle’s square roots on Hoop algebras

Document Type : Research Paper

Authors

Mohammad Mahdi Motamedi Nezhad

Ali Madanshekaf

Department of Mathematics, Semnan University, Semnan, Iran

10.22103/jmmr.2026.26238.1897

Abstract

In this article, we use the square root as a 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 to 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 some relationships with other classes of ordered algebras such as Boolean algebras and Gödel algebras are explored. Several examples are provided as well. Ultimately, it is shown that the class of all (good) bounded V-hoop algebras with square roots is a variety.

Keywords

Hoop algebra

Wajsberg hoop

Basic hoop

Good hoop

Gödel algebra

(Strict) Square root

n-th root

Subjects

Mathematics

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