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1)  subdirectly irreducible ring
亚直不可约环
1.
On some characters of the upper radical determined by the class of all J - semisimple subdirectly irreducible rings;
关于由J-半单的亚直不可约环类所确定的刻划
2.
The essential rings are defined,and it is also the generalization of both the subdirectly irreducible rings and the prime rings.
定义了本质环 ,它同时是亚直不可约环和素环的推广 ;给出了本质环的一些描述及基本性质 ;研究了由本质环所决定的两个特殊根 。
3.
In this paper, let σ be an arbitrary suppernilpotent radical, the upper radical detemined by the class of all σ-semisimple subdirectly irreducible rings is studied.
研究了任一个超幂零根为零的亚直不可约环所确定的环类 ,证明了由这样的环类所确定的上根都是特殊根 ,并且给出了这类根的一些刻
2)  subdirectly irreducible
次直不可约
1.
Suppose that N is a zero-product-associative distributively generated near-ring,it is shown that(i) if N is a subdirectly irreducible and has no nonzero nilpotent element of index 2,then N is integral,and(ii) N is a subdirect product of zero-product-associative distributively generated near-rings if and .
设N是零积结合分配生成近环,本文证明了:(i)如果N是次直不可约的且无非零的二次幂零元,则N是整的;(ii)N是零积结合分配生成整近环的次直积当且仅当N不含非零的二次幂零元。
3)  subdirectly irreducible ring
亚直既约环
1.
The author give certain sufficient or necessary conditions on a class M of subdirectly irreducible rings for UM satisfies property (Int).
讨论了由亚直既约环类所确定的上根,给出了满足条件(b)的上根的一些刻
2.
This paper deals with some retative properties of A and smash product A#G * ; when A is graded faithful, A#G * is subdirectly irreducible ring if and only if A e is also.
讨论了分次环A,Ae和A#G*的相关性质,在A是分次忠实时,A#G*是亚直既约环当且仅当Ae是亚直既约环;在A是分次非退化时,A#G*是G亚直既约环当且仅当A是分次亚直既约环。
3.
In the present note we first prove that every subdirectly irreducible ring can beobtained as a homomorphic image of another subdirectly irreducible ring and then point outan example of a subdirectly irreducible ring R with heart H for which:(1) R has a non-subdirectly irreducible homomorphic image.
本文证明了每一个亚直既约环能够作为另一个亚直既约环的真同态象。
4)  irreducible decomposition
不可约分解
1.
The irreducible decomposition of the Product of all elements in gvien table basis of a table algebra;
表代数全体表基元乘积的不可约分解
5)  irreducible fraction
不可约分数
6)  quadratic factor
二次不可约因式
1.
By using the result of Lucas number primitive divisor,as n>max{30,12(|b|+1)},it receives all f(x) of irreducible quadratic factors with integer coefficients when the first coefficient equals 1.
本文研究了三项式f(x)=xn-bx+a的二次不可约因式,利用Lucas数本原素因数的存在性的结果,对于n≥max(30,(|b|+1)/2)的情况,得到了所有含有首项系数等于1的二次整系数不可约因式的f(x)。
补充资料:翰林权直罢归和朱约山韵
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