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- 주제어 : exchange ideal (검색결과 13 건)
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ON THE PUBLIC KEY CRYPTOSYSTEMS OVER CLASS SEMIGROUPS OF IMAGINARY QUADRATIC NON-MAXIMAL ORDERS
Kim, Young-Tae,Kim, Chang-Han Korean Mathematical Society 2006 대한수학회논문집 Vol.21 No.3
In this paper we will propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structures of class SEMIGROUPS of imaginary quadratic orders which were given by Zanardo and Zannier [8], and we will give a general algorithm for calculating power of ideals/classes via the Dirichlet composition of quadratic forms which is applicable to cryptography in the class semigroup of imaginary quadratic non-maximal order and revisit the cryptosystem of Kim and Moon [5] using a Zanardo and Zannier [8]'s quantity as their secret key, in order to analyze Jacobson [7]'s revised cryptosystem based on the class semigroup which is an alternative of Kim and Moon [5]'s.
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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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CHEN, HUANYIN Korean Mathematical Society 2005 대한수학회보 Vol.42 No.2
In this paper, we investigate exchange ideals and get some new characterization of exchange rings. It is shown that an ideal I of a ring R is an exchange ideal if and only if so is $QM_2$(I). Also we observe that every exchange ideal can be characterized by exchange elements.
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CHEN, HUANYIN,CHEN, MIAOSEN Korean Mathematical Society 2005 대한수학회보 Vol.42 No.1
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.
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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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ON QUASI-STABLE EXCHANGE IDEALS
Chen, Huanyin Korean Mathematical Society 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 $M_n$(I) as an ideal of $M_n$(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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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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On QB-ideals of exchange rings
Huanyin Chen 대한수학회 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 2×2 matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange QB-rings are studied as well. We characterize QB-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every 2×2 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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ON THE STRUCTURES OF CLASS SEMIGROUPS OF QUADRATIC NON-MAXIMAL ORDERS
KIM, YONG TAE The Honam Mathematical Society 2004 호남수학학술지 Vol.26 No.3
Buchmann and Williams[1] proposed a key exchange system making use of the properties of the maximal order of an imaginary quadratic field. $H{\ddot{u}}hnlein$ et al. [6,7] also introduced a cryptosystem with trapdoor decryption in the class group of the non-maximal imaginary quadratic order with prime conductor q. Their common techniques are based on the properties of the invertible ideals of the maximal or non-maximal orders respectively. Kim and Moon [8], however, proposed a key-exchange system and a public-key encryption scheme, based on the class semigroups of imaginary quadratic non-maximal orders. In Kim and Moon[8]'s cryptosystem, a non-invertible ideal is chosen as a generator of key-exchange ststem and their secret key is some characteristic value of the ideal on the basis of Zanardo et al.[9]'s quantity for ideal equivalence. In this paper we propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structure of the class semigroup of non-maximal order as finitely disjoint union of groups with some quantities correctly. And then we correct the misconceptions of Zanardo et al.[9] and analyze Kim and Moon[8]'s cryptosystem.
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