Quasigroups and loops are studied in four research areas; algebra, geometry, topology and
combinatorics. We shall be discussing them in the direction of algebra. Let G be a non …

In this paper, the holomorphic study of inverse properties in loops is put in a more general
setting. For various combinations of r, s, t∈ ℤ in parities, it was established that:(i) the A (Q) …

This monograph is a compilation of results on some new Smarandache concepts in
Smarandache; groupoids, quasigroups and loops, and it pin points the inter-relationships …

Abstract A loop (GH,·) is called a special loop of the loop (G,·) if the pair (H,·) is an arbitrary
non-trivial subloop of (G,·). In particular,(GH,·) is called a second Smarandache Bol loop …

Let (G,·) be a loop. A loop (GH,·) is called a special loop of (G,·) if the pair (H,·) is an arbitrary
a non-empty subloop of (G,·). In general,(GH,·) is called second Smarandache Bol loop …

Page 1 International Journal of Mathematical Analysis and Optimization: Theory and
Applications Vol. 2019 , pp. 426 - 432 Holomorph of self-distributive quasigroup with key …

By studying the holomorphic structure of automorphic inverse property quasigroups and
loops [AIPQ and (AIPL) and cross inverse property quasigroups and loops [CIPQ and …

A loop (Q,∙) is called a Basarab loop if the identities:(x∙ yx ρ)∙(xz)= x∙ yz and (yx)∙(x λ z∙ x)= yz∙
x hold. The holomorphy of a Basarab loop Q was investigated with respect to a group A (Q) …

The present study further strengthens the use of the Keedwell CIPQ against attack on a
system by the use of the Smarandache Keedwell CIPQ for cryptography in a similar spirit in …

A Smarandache quasigroup (loop) is shown to be universal if all its f, g-principal isotopes
are Smarandache f, g-principal isotopes. Also, weak Smarandache loops of Bol-Moufang …