第二类Smarandache Bol环的基本性质
Basic Properties Of Second Smarandache Bol Loops
摘要：
如果$(G,\cdot)$是一个带有任意子循环$(H,\cdot)$的循环，则将对$(G_H,\cdot)$称为特殊循环。一个特殊的循环$(G_H,\cdot)$被称为第二Smarandache Bol循环（S $_{2^{\tiny\textrm{nd}}}$ BL），当且仅当它对于$H$中的所有$x,z$和$G$中的所有$s$都服从第二Smarandache Bol恒等式$(xs\cdot z)s=x(sz\cdot s)$。被称为Bol循环的广为人知且研究充分的循环类属于这类，因此S $_{2^{\tiny\textrm{nd}}}$ BL推广了Bol循环。研究了S $_{2^{\tiny\textrm{nd}}}$ BL的基本性质。这些属性在性质上都是Smarandache。在这项工作中的结果推广了Bol循环的基本性质，发现在博士。D的论文。a.罗宾逊提出了一些有待进一步研究的问题。
英文摘要：
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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