RISS 검색 - 국내학술지논문

1
ON EXCHANGE qb-IDEALS

CHEN, HUANYIN,CHEN, MIAOSEN Korean Mathematical Society 2005 대한수학회보 Vol.42 No.1
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In this paper, we establish necessary and sufficient conditions for an exchange ideal to be a qb-ideal. It is shown that an exchange ideal I of a ring R is a qb-ideal if and only if when-ever $a{\simeq}b$ via I, there exists u ${\in} I_q^{-1}$ such that a = $ubu_q^{-1}$ and b = $u_q^{-1}$. This gives a generalization of the corresponding result of exchange QB-rings.
2
EXCHANGE RINGS SATISFYING STABLE RANGE CONDITIONS

Chen, Huanyin,Chen, Miaosen Korean Mathematical Society 2002 대한수학회보 Vol.39 No.2
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In this paper, we establish necessary and sufficient conditions for an exchange ring R to satisfy the n-stable range condition. It is shown that an exchange ring R satisfies the n-stable range condition if and only if for any regular a $\in$ R$^n$, there exists a unimodular u $\in$$^n$ R such that au $\in$ R is a group member, and if and only if whenever a$\simeq$$_n$b with a $\in$ R, b $\in$ M$_n$(R), there exist u $\in$ R$^n$, v $\in$$^n$ R such that a = ubv with uv = 1. As an application, we observe that exchange rings satisfying the n-stable range condition can be characterized by Drazin inverses. These also give nontrivial generalizations of [7, Theorem 10], [13, Theorem 10], [15, Theorem] and [16, Theorem. 2A].
3
Exchange rings satisfying stable range conditions

Huanyin Chen,Miaosen Chen 대한수학회 2002 대한수학회보 Vol.39 No.2
In this paper, we establish necessary andsufficient conditions for an exchange ring R to satisfy then-stable range condition. It is shown that an exchange ring Rsatisfies the n-stable range condition if and only if for anyregular ain R^n, there exists a unimodular uin ^nR such thatauin R is a group member, and if and only if wheneveraoverline{sim}_nb with ain R, bin mbox{M}_n(R), thereexist uin R^n, vin ^nR such that a=ubv with uv=1. As anapplication, we observe that exchange rings satisfying then-stable range condition can be characterized by Drazininverses. These also give nontrivial generalizations of [7,Theorem 10], [13, Theorem 10], [15, Theorem] and [16, Theorem 2A].
4
On exchange qb-ideals

Huanyin Chen,Miaosen Chen 대한수학회 2005 대한수학회보 Vol.42 No.1
In this paper, we establish necessary and sufficientconditions for an exchange ideal to be a qb-ideal. It is shownthat an exchange ideal I of a ring R is a qb-ideal if andonly if whenever a{overline sim}b via I, there exists uinI_q^{-1} such that a=ubu_q^{-1} and b=u_q^{-1}au. This givesa generalization of the corresponding result of exchangeQB-rings.

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