A new representation of finite Hoops using a new type of product of structures

Michal Botur

doi:10.1007/s11225-025-10181-1

paper

A new representation of finite Hoops using a new type of product of structures

arXiv:2511.06730 · doi:10.1007/s11225-025-10181-1

Abstract

In this paper we show that a new type of products hoops can be defined which, in the case of finite hoops, can describe an arbitrary hoop $A$ as the product of its arbitrary filter $F$ and the corresponding homomorphic image $A / F$ . Moreover, this product satisfies a certain kind of associativity, and as a consequence we show that every finite hoop is in this sense a product of finite MV-chains.

16 pages, 5 figures