Basic Properties Of Second Smarandache Bol Loops

Details Basic Properties Of Second Smarandache Bol Loops Basic Properties Of Second Smarandache Bol Loops

2010-03-06

arxiv.org/abs/1003.1382v1

International Journal of Mathematical Combinatorics, Vol. 2 (2009), 11-20.

Mathematics

General Mathematics

10 pages

Scientific paper

The pair $(G_H,\cdot)$ is called a special loop if $(G,\cdot)$ is a loop with an arbitrary subloop $(H,\cdot)$. A special loop $(G_H,\cdot)$ is called a second Smarandache Bol loop(S$_{2^{{\tiny\textrm{nd}}}}$BL) if and only if it obeys the second Smarandache Bol identity $(xs\cdot z)s=x(sz\cdot s)$ for all $x,z$ in $G$ and $s$ in $H$. The popularly known and well studied class of loops called Bol loops fall into this class and so S$_{2^{{\tiny\textrm{nd}}}}$BLs generalize Bol loops. The basic properties of S$_{2^{{\tiny\textrm{nd}}}}$BLs are studied. These properties are all Smarandache in nature. The results in this work generalize the basic properties of Bol loops, found in the Ph.D. thesis of D. A. Robinson. Some questions for further studies are raised.

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