Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters

Abstract

We study hoops in order to give some new characterizations for regular and Boolean elements in hoops and we study the relationship between them. Specially, we prove that any bounded v-hoop is a Stone algebra if and only if MV -center set and Boolean elements set are equal. Then we define the concept of regular filter in hoops and v-hoops with RF-property and peruse some properties of them. In addition, we show that each v-hoop with RF-property, is a Boolean algebra and any hoop A with RF-property such that B(A) = {0, 1}, is a local hoop. Finally, we prove that any hoop A has RF-property if and only if Spec(A) = Max(A) and if and only if A is a hyperarchimedean. © 2023 M. Aaly Kologani et al., published by Sciendo.