Smarandache Isotopy Theory Of Smarandache: Quasigroups And Loops

TL;DR

This paper introduces and explores Smarandache isotopy theory for algebraic structures like groupoids, quasigroups, and loops, extending classical isotopy concepts to Smarandache structures.

Contribution

It develops the theory of Smarandache isotopy, including classes, principal isotopes, and G-Smarandache loops, advancing the understanding of these algebraic structures.

Findings

Defined Smarandache isotopy and isomorphy classes

Analyzed Smarandache principal isotopes

Studied properties of G-Smarandache loops

Abstract

The concept of Smarandache isotopy is introduced and its study is explored for Smarandache: groupoids, quasigroups and loops just like the study of isotopy theory was carried out for groupoids, quasigroups and loops. The exploration includes: Smarandache; isotopy and isomorphy classes, Smarandache $f,g$ principal isotopes and G-Smarandache loops.