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强半单根
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  strongly semisimple radicals
     Hereditary Radicals and Strongly Semisimple Radicals in Normal Classes of Algebras
     代数正规类中的遗传根与强半单根(英文)
短句来源
  strong semisimple radical
     Let R be a radical,then R is a strong Semisimple radical if and only if the following conditionis fulfilled: For evers ideal Ⅰ of an arbitrary A Ⅰ= I + R (A) holds.
     设R是一个根,则R是一个强半单根的充分必要条件是满足对任意环A的每一个理想I,I=I+R(A)成立。 Ⅱ.
短句来源
     Abstract This paepr gives concepts on the close radical for intersection of ideals and second-rate strong semisimple radical F.
     本文给出了交封闭根和次强半单根的概念,解决了F.
短句来源
  “强半单根”译为未确定词的双语例句
     On the Close Radical for Intersection andSecond-Rate Strong Semlisimpe Radical
     关于交封闭根的次强半单根
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  相似匹配句对
     On the Close Radical for Intersection andSecond-Rate Strong Semlisimpe Radical
     关于交封闭根的次单根
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     ON STRONG SEMI-NORMALITY
     关于正规性
短句来源
     Semi-regularity Strong Fuzzy Compactness
     正则F紧性
     Hereditary Radicals and Strongly Semisimple Radicals in Normal Classes of Algebras
     代数正规类中的遗传根与单根(英文)
短句来源
     Abstract This paepr gives concepts on the close radical for intersection of ideals and second-rate strong semisimple radical F.
     本文给出了交封闭根和次单根的概念,解决了F.
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In this paper, we prove following main rosults I. Let R be a radical,then R is a strong Semisimple radical if and only if the following conditionis fulfilled: For evers ideal Ⅰ of an arbitrary A Ⅰ= I + R (A) holds. II. Let R be a radical and A an arbitry ring, then the following condit-ions are equivalent: 1. let I_1, I_2 be arbitrary ideals of a ring A,then I_1∩I_2= I_1∩I_2 holds 2. let I be an ideal of an arbitrary ring A, the T_i is a convex suh-la-ttice of L (A) andβ(A) is a lower semi-lattice with T_(i_1)T_(i_2)=...

In this paper, we prove following main rosults I. Let R be a radical,then R is a strong Semisimple radical if and only if the following conditionis fulfilled: For evers ideal Ⅰ of an arbitrary A Ⅰ= I + R (A) holds. II. Let R be a radical and A an arbitry ring, then the following condit-ions are equivalent: 1. let I_1, I_2 be arbitrary ideals of a ring A,then I_1∩I_2= I_1∩I_2 holds 2. let I be an ideal of an arbitrary ring A, the T_i is a convex suh-la-ttice of L (A) andβ(A) is a lower semi-lattice with T_(i_1)T_(i_2)= T_(i_1∩I_2). Ⅲ. let R bea radical and A aring, then the following conditions ate eq-uivalent: 1. let I_1, I_2 be arbitrary ideals of a ring A,then R (I_1 +I_2) = R (I_1) +R (I_2) holds. 2. let I be an ideal of an arbitrary ring A, then T_i is a covex uppersub-semi-lattice and D is an upper semi-lattice with T_(I_1)? T_(I_2) = T_(I_1+I_2)

本文证明了下面主要结果: Ⅰ.设R是一个根,则R是一个强半单根的充分必要条件是满足对任意环A的每一个理想I,I=I+R(A)成立。Ⅱ.设R是一个根,A是任意环,则下面条件等价。(1)?I_1,I_2?A有I_1∩I_2=I_1∩I_2; (2)?I?A,T_I是L(A)的凸子格且β(A)是一个下半格,其中T_(I_1)∩T_(I_2)=T_(I_1∩I_2) Ⅲ.设R是一个根,A是任意环,则下面条件等价。(1)?I_1,I_2?A均满足R(I_1+I_2)=R(I_1)+R(I_2); (2)?I?A,T_I是L(A)的凸子上半格,D是上半格且T_(I_1)∨T_(I_2)=T_(I_1+I_2)(?I_2,I_2? A) 本文中的根,如不特别声明,一概指Amisur-Kypow意义下的根,下面所指的环均为结合环。

Abstract This paepr gives concepts on the close radical for intersection of ideals and second-rate strong semisimple radical F. A. SZasz's open problem 14 is solved

本文给出了交封闭根和次强半单根的概念,解决了F.A.SZáSZ的公开问题14.

Puczylowski established the general theory of radicals of the class of objects called algebras. In this paper, we make use of the method of lattice theory to characterize the general hereditary radicals and general strongly semisimple radicals and investigate some properties of them in normal classes of algebras. This extends some known studies on the theory of radicals of various algebraic strutures.

Puczylowski建立了一般代数对象类的根理论.本文在代数正规类中,用格论方法刻划一般遗传根和强半单根类,探究它们的一些性质,推广了已知各类代数系统的某些根论研究.

 
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