1) graded ring
分次环
1.
It introduces a new conception—augmented(G,H)-graded rings,give two characterizatons for augmented(G,H)-graded rings in special cases.
将扩大G-分次环的概念加以推广,定义了一种新的分次环——扩大(G,H)-分次环,给出其两个等价刻划,并在R(G,H)-A g r中引入N oetherian模的概念,讨论了R(G,H)-A g r与(Re,H)-g r范畴间N oetherian模的一些性质与关系。
2.
The BrownMcCoy radicals of the graded rings are studied.
研究了分次环的Brown-McCoy根,用新的方法证明并推广了文献[1]中的主要结果,证明在比自由群更广泛的群类上分次环的Brown-McCoy根是分次的。
3.
In this note ,we characterize the graded Bear radical,graded koethe radical,graded Levitizki radical and graded Brown-McCoy radical in the category of associative monoid-graded rings (not necessarily with 1) and grade-preserving ring homomorphisms,with element properties.
在一般Monoid—分次环 (未必有 1)范畴中 ,给出了分次Bear根 ,分次Koethe根 ,分次Levitizki根和分次Brown -McCoy -根的元素特性 ,并分别给出了对应于这几个根的分次半单环的结构定理 ,指出了分次环A = x∈MAx 的分次根和结合环Ae 的根之间的密切关系。
2) graded PS-ring
分次PS-环
1.
We prove that S is a graded right V-ring if and only if R is a graded right V-ring,S is graded PS-ring if and only if R is a graded PS-ring,and S is a Von Neumann regular ring if and only if R is a graded Von Neumann regular ring.
本文引进了分次环的分次Excellent扩张概念,设S=⊕_(g∈G)S_g是R=⊕_(g∈G)R_g的分次Excellent扩张,证明了S是分次右V-环当且仅当R是分次右V-环,S是分次PS-环当且仅当R是分次PS-环,S是分次Von Neumann正则环当且仅当R是分次Von Neumann正则环。
3) H-graded ring
H-分次环
1.
Let R be a G-graded ring with local units,if we view H-graded rings R#G/H as-setH/K-graded rings,then we will get the category(H/K,R#G/H)-gr is isomorphic to the category(G/K,R)-gr.
若R是具有局部单位元的G-分次环则可将H-分次环自然地看成H-集H/K-分次环,得到H/K-分次-模范畴(H/K,)-gr与G/K-分次R-模范畴(G/K,R)-gr同构。
4) M-graded ring
M-分次环
5) group-graded ring
群分次环
1.
Duality theorems for group-graded rings in double products;
群分次环上双积对偶定理
2.
In this paper we devoted to study the socles and graded socles of group-graded rings and modules.
本文的主要目的是研究群分次环与群分次模的基座和分次基座，获得了有关环与模的Jacobson根的对偶的一些主要结果，推广了关于交叉积的一些相关结果。
6) group graded ring
群分次环
1.
In this paper, the main results about the socles of crossed products are generalized to group graded rings.
将关于交叉积的基座的主要结果推广到了群分次环上 ,得到了群分次环的基座的一些具体刻划 ,特别地 ,证明了对有限群G和强G 分次环R ,有Soc(RR) Soc(ReRe)R soc｜G｜(RR) 。
补充资料：分次
1.分定等次或位次。 2.指分为几次。 3.星辰运行的度次。
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