1) left V-rings
左V-环
1.
Next,left V-rings were characterized by simple-projective modules;At last,Schanuel Lemma of relatively simple-projective modules was proved.
引进了单投射模的概念,给出了单投射模的等价条件,并讨论了它的一些性质;进一步地,给出了左SP-环的定义,证明了SP-环是Morita不变的;接着,利用单投射模刻画了左V-环;最后给出了相对于单投射模的Schanuel引理。
2) left ring
左环
1.
It is proved that V-idempotent semiring is normal if and only if it is a pseudo-strong right normal idempotent semiring of left zero semirings,and the direct product of left normal V-idempotent semiring with a ring is a pseudo-strong semilattice idempotent semiring of left rings,and some corollaries.
证明了V-幂等半环是正规的当且仅当它是左零半环的伪强右正规幂等半环,并得出左正规V-幂等半环与环的直积是左环的伪强半格幂等半环,及相关结论。
2.
This result last gets the characterization of the direct product of left normal A-idempotent semiring and a ring as a pseudo-strong semilattice idempotent semiring of left rings,and some corollaries.
构造了C 半环的伪强右正规幂等半环的结构,证明了A 幂等关环是正规幂等半环,当且仅当它是左零半环的伪强右正规幂等半环,得出这类幂等关环与环的直积是左环的伪强半格幂等关环及相关结论。
3.
and this kind of idempotent semiring is a pseudo-strong right normal idempotent semiring of left zero semirings,This result gets the characterization of the direct product of this kind of idempotent sermiring and a ring as a pseudo-strong right normal idempotent semiring of left rings.
本文讨论了满足a+ab=a+b的幂等半环的结构,给出这种幂等半环是左零半环的伪强右正规幂等半环,并得出这种幂等半环与环的直积是左环的伪强右正规幂等半环。
3) V-ring
V-环
1.
The author determines necessary and sufficient conditions for a forinal triangular matrix ring to be V-ring or semi- V-ring.
本文研究形式三角矩阵环 R 的若干新性质,讨论 R-模的伪投射性,给出了形式三角矩阵环 R 是 V-环或半 V-环的充要条件。
2.
A new generalization of V-rings is given by terms of quasi-dual module.
定义了quasi-dual模,讨论了它的性质和等价条件,并且通过quasi-dual模,详细讨论了V-环的一个新的推广结构,得到了以下等价条件:1R/Soc(RR)是右V-环;2每一个R的本质真右理想是极大右理想的交;3存在一个奇异半单右R-模是quasi-dual的。
4) V ring
V-环
1.
Introduces and characterizes graded V rings proves that a graded ring R and the rings which are derived by it, R,Re,R#G are identical on the properties about V rings on the conditions of finite group G type strongly graded ring (| G | is inverse of R , e is the identity of G ).
引入并刻划了分次 V-环 ,证明在有限群 G-型强分次环 (|G|是 R的逆元 ,e是 G的单位元 )的条件下 ,分次环 R及由它导出的非分次环 R,Re,R# G在 V-环性质上是一致的 。
2.
Some characterizations of cofinitely related modules are given,conoetherian rings and V rings are characterized by cofinitely related modules,some conditions under which coregular rings are V rings are given,a condition under which left hereditary rings are semisimple rings is given too.
给出了有限余相关模的刻画 ,用有限余相关模刻画了余 Noether环和 V-环 ,给出了余正则环为 V-环的条件和遗传环为半单环的一个条件 。
5) left heart circulation
左心循环
1.
RESULTS: In the volume graph, the effect of left heart circulation was (54.
结果:在容积图中左心循环作用为(54。
2.
The model contains left ventricle(LV),left atrium,systemic circulation,aortic valve and mitral valve;it simulated the hemodynamics phenomena of left heart circulation.
将左心模型与四元件的动脉系统Windkessel模型耦合,构成左心-动脉系统交互的左心循环系统模型。
6) left zero semiring
左零半环
1.
It is proved that V-idempotent semiring is normal if and only if it is a pseudo-strong right normal idempotent semiring of left zero semirings,and the direct product of left normal V-idempotent semiring with a ring is a pseudo-strong semilattice idempotent semiring of left rings,and some corollaries.
证明了V-幂等半环是正规的当且仅当它是左零半环的伪强右正规幂等半环,并得出左正规V-幂等半环与环的直积是左环的伪强半格幂等半环,及相关结论。
2.
In this paper,we construct the structure of the pseudo-strong right normal idempotent semiring of C-semirings,and then an A-idempotent semiring is a normal idempotent semiring,if and only if it is a pseudo-strong right (normal) idempotent semiring of left zero semirings.
构造了C 半环的伪强右正规幂等半环的结构,证明了A 幂等关环是正规幂等半环,当且仅当它是左零半环的伪强右正规幂等半环,得出这类幂等关环与环的直积是左环的伪强半格幂等关环及相关结论。
3.
and this kind of idempotent semiring is a pseudo-strong right normal idempotent semiring of left zero semirings,This result gets the characterization of the direct product of this kind of idempotent sermiring and a ring as a pseudo-strong right normal idempotent semiring of left rings.
本文讨论了满足a+ab=a+b的幂等半环的结构,给出这种幂等半环是左零半环的伪强右正规幂等半环,并得出这种幂等半环与环的直积是左环的伪强右正规幂等半环。
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