1) torsion free
挠自由
1.
We prove that all regular left S-acts are torsion free iff, for every e~2=e∈S and every left cancelable element r∈S, there is a t∈S such that tre=e.
本文证明了所有正则左S 系是挠自由的当且仅当对每个元e2 =e∈S和每个S中的左消元r,必存在元t∈S,使得tre=e,从而改进了文献[4]的一个结果。
2.
It is Proved that all torsion free right S\|acts satisfy condition (P\-T) if and only if S is a left, Almost regular monoid, and that all right S\|acts satisfy condition (P\-T) if and only if S is a regular monoid.
证明了所有挠自由右S-系满足条件(PT)当且仅当S是左几乎正则幺半群;所有右S-系满足条件(PT)当且仅当S是正则幺半群。
3.
A sufficient and necessary condition for all right torsion free acts satisfying condition(Q) is given.
研究条件 (P)的推广形式 (条件 (Q) )及其对幺半群的刻画 ,给出了所有挠自由右S 系满足条件 (Q)的充要条件 。
2) torsion-free
挠自由的
1.
Let N be a zero-symmetric prime nearring,got the following results:(ⅰ)If N is 2-torsion-free,d_1 and d_2 are derivatins of N,then the following three conditions are equivalent:(1)d_1d_2 is a derivation;(2)d_1(x)d_2(y)+d_2(x)d_1(y)=0,x,y∈N;(3)either d_1=0 or d_2=0.
设N是零对称的素拟环,证明了:(ⅰ)若N是2-挠自由的,d1,d2是N上的两个导子,则下列3条件等价:(1)d1d2是一个导子;(2)d1(x)d2(y)+d2(x)d1(y)=0,x,y∈N;(3)d1=0或d2=0。
3) 2-torsion
2-挠自由
4) n-torsionfree modules
挠自由模
1.
This paper,using properties of n-torsionfree modules,first gives an equivalent characterization of Noether rings satisfying W(n) condition.
用挠自由模类的性质刻画了Noether环上的W(n)条件,并研究了其对称性;给出了满足W(n)条件和具有限自内射维数的等价的一些条件;最后通过环的右极小内射分解给出了全体左模范畴的内射上生成子。
5) torsion-free Z-module
挠自由Z-模
6) 2-torsion-free
2-挠自由的
1.
Let N be a zero-symmetric prime nearring,got the following results:(ⅰ)If N is 2-torsion-free,d_1 and d_2 are derivatins of N,then the following three conditions are equivalent:(1)d_1d_2 is a derivation;(2)d_1(x)d_2(y)+d_2(x)d_1(y)=0,x,y∈N;(3)either d_1=0 or d_2=0.
设N是零对称的素拟环,证明了:(ⅰ)若N是2-挠自由的,d1,d2是N上的两个导子,则下列3条件等价:(1)d1d2是一个导子;(2)d1(x)d2(y)+d2(x)d1(y)=0,x,y∈N;(3)d1=0或d2=0。
补充资料：必然王国与自由王国(见必然与自由)
必然王国与自由王国(见必然与自由)
realm of necessity and realm of freedom
of口1 Iun Wongg口0 yU ZlyQU wangguo必然王国与自由王国(realmandrealm of freedom)necessity见必然与自由。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条