摘要
得到了圈Ｇ可适当定义序。
necessary and sufficient condition for a loop(G,+)to be a po-loop(G,+,≤)is ob-tained. The following theorem is proved。Theorem Any po-loop G is determined to within isomorphism by its positive cone P=G￣+,Since(*)a≤b,b─a∈P,-a+b∈P,b+(-a)∈P,(一a)+b∈P are equivalent conditions. Moreover C_1)0 ∈P; C_2) if x,y ∈P then x+y∈P; C_3)if x,y∈P and x+y=0 then x=y=0; C_4)if a─b,c─d∈P then(a─d)─(b─c),(a+(─d))─(b+(─c)),(─d+a)──c十b)∈P, Conversely,if G is any loop,and P is a subset of G satisfying C_1)～C_4),then the condition(*)defines G as a po-loop.
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
1995年第1期17-19,共3页
Journal of Inner Mongolia University：Natural Science Edition
基金
内蒙古自然科学基金
关键词
圈
正锥
群
po圈
loop po-loop positive cone of po-loop
