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- 저자 : Huanyin Chen (검색결과 42 건)
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ELEMENTARY MATRIX REDUCTION OVER ZABAVSKY RINGS
Chen, Huanyin,Sheibani, Marjan Korean Mathematical Society 2016 대한수학회보 Vol.53 No.1
We prove, in this note, that a Zabavsky ring R is an elementary divisor ring if and only if R is a $B{\acute{e}}zout$ ring. Many known results are thereby generalized to much wider class of rings, e.g. [4, Theorem 14], [7, Theorem 4], [9, Theorem 1.2.14], [11, Theorem 4] and [12, Theorem 7].
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ON QUASI-STABLE EXCHANGE IDEALS
Huanyin Chen 대한수학회 2010 대한수학회지 Vol.47 No.1
We introduce, in this article, the quasi-stable exchange ideal for associative rings. If I is a quasi-stable exchange ideal of a ring R, then so is Mn(I) as an ideal of Mn(R). As an application, we prove that every square regular matrix over quasi-stable exchange ideal admits a diagonal reduction by quasi invertible matrices. Examples of such ideals are given as well.
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Huanyin Chen 대한수학회 2008 대한수학회지 Vol.45 No.3
In this paper, we introduce a new class of rings, SB-rings. Weestablish various properties of this concept. These shows that, in severalrespects, SB-rings behave like rings satisfying unit 1-stable range. Wewill give necessary and sufficient conditions under which a semilocal ringis a SB-ring. Furthermore, we extend these results to exchange ringswith all primitive factors artinian. For such rings, we observe that theconcept of the SB-ring coincides with Goodearl–Menal condition. Thesealso generalize the results of Huh et al., Yu and the author on ringsgenerated by their units
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UNIT-REGULARITY AND STABLE RANGE ONE
Huanyin Chen 대한수학회 2010 대한수학회보 Vol.47 No.3
Let R be a ring, and let Ψ(R) be the ideal generated by the set {x ∈ R | 1 + sxt ∈ R is unit-regular for all s, t ∈ R}. We show that Ψ(R) has “radical-like” property. It is proven that Ψ(R) has stable range one. Thus, diagonal reduction of matrices over such ideal is reduced.
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On separative refinement monoids
Huanyin Chen 대한수학회 2009 대한수학회보 Vol.46 No.3
We obtain two new characterizations of separativity of refinement monoids, in terms of comparability-type conditions. As applications, we get several equivalent conditions of separativity for exchange ideals. We obtain two new characterizations of separativity of refinement monoids, in terms of comparability-type conditions. As applications, we get several equivalent conditions of separativity for exchange ideals.
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ON SEPARATIVE REFINEMENT MONOIDS
Chen, Huanyin Korean Mathematical Society 2009 대한수학회보 Vol.46 No.3
We obtain two new characterizations of separativity of refinement monoids, in terms of comparability-type conditions. As applications, we get several equivalent conditions of separativity for exchange ideals.
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UNIT-REGULARITY AND STABLE RANGE ONE
Chen, Huanyin Korean Mathematical Society 2010 대한수학회보 Vol.47 No.3
Let R be a ring, and let $\Psi$(R) be the ideal generated by the set {x $\in$R | 1 + sxt $\in$ R is unit-regular for all s, t $\in$ R}. We show that $\Psi$(R) has "radical-like" property. It is proven that $\Psi$(R) has stable range one. Thus, diagonal reduction of matrices over such ideal is reduced.
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Weakly stable conditions for exchange rings
Huanyin Chen 대한수학회 2007 대한수학회지 Vol.44 No.4
A ring R has weakly stable range one provided that aR +bR = R implies that there exists ay 2 R such that a + by 2 R is rightor left invertible. We prove, in this paper, that every regular elementin an exchange ring having weakly stable range one is the sum of anidempotent and a weak unit. This generalize the corresponding result ofone-sided unit-regular ring. Extensions of power comparability and powercancellation are also studied.1. IntroductionA ring R is said to be an exchange ring if for every rightR-module A andany two decompositionsA = M N =Li2 I Ai, whereMR = RR and I is anite index set, there exist submodulesA0i Ai such thatA = M (Li2 I A0i).It is well known that regular rings,-regular rings, unitC-algebras of realrank zero, semiperfect rings, left or right continuous rings and clean rings areall exchange rings. For general theory of exchange rings, we refer the readersto [10]. Following Wei and Tong (cf. [11]), a ringR is said to have weakly
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ON QB-IDEALS OF EXCHANGE RINGS
Chen, Huanyin Korean Mathematical Society 2009 대한수학회보 Vol.46 No.5
We characterize QB-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every $2\times2$ matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange QB-rings are studied as well.
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PIERCE STALKS OF EXCHANGE RINGS
Huanyin Chen 대한수학회 2010 대한수학회지 Vol.47 No.4
We prove, in this article, that a ring R is a stable exchange ring if and only if so are all its Pierce stalks. If every Pierce stalks of R is artinian, then 1R = u + v with u, v ∈ U(R) if and only if for any a ∈ R, there exist u, v ∈ U(R) such that a = u + v. Furthermore, there exists u ∈ U(R) such that 1R ± u ∈ U(R) if and only if for any a ∈ R,there exists u ∈ U(R) such that a ± u ∈ U(R). We will give analogues to normal exchange rings. The root properties of such exchange rings are also obtained.
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