• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.1-6
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• 1994

In this paper, some properties for a PI-ring satisfying the descending chain condition on essential left ideals are studied: Let R be a ring with a polynomial identity satisfying the descending chain condition on essential ideals. Then all minimal prime ideals in R are maximal ideals. Moreover, if R has only finitely many minimal prime ideals, then R is left and right Artinian. Consequently, if every primeideal of R is finitely generated as a left ideal, then R is left and right Artinian. A finitely generated PI-algebra over a commutative Noetherian ring satisfying the descending chain condition on essential left ideals is a finite module over its center.(omitted)

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.239-248
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• 2021

In this paper we study modules with the W F I⁺-extending property. We prove that if M satisfies the W F I⁺-extending, pseudo duo properties and M/(Soc M) has finite uniform dimension then M decompose into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if M satisfies the W F I⁺-extending, pseudo duo properties and ascending chain (respectively, descending chain) condition on essential submodules then M = M₁ ⊕ M₂ for some semisimple submodule M₁ and Noetherian (respectively, Artinian) submodule M₂. Moreover, we show that if M is a W F I-extending module with pseudo duo, C₂ and essential socle then the quotient ring of its endomorphism ring with Jacobson radical is a (von Neumann) regular ring. We provide several examples which illustrate our results.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1163-1173
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• 2021

In this paper, we obtain the MacWilliams identity for linear codes over finite chain rings with respect to homogeneous weight, and the product of chain rings.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1257-1268
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• 2018

In this article we first investigate a sort of unit-IFP ring by which Antoine provides very useful information to ring theory in relation with the structure of coefficients of zero-dividing polynomials. Here we are concerned with the whole shape of units and nilpotent elements in such rings. Next we study the properties of unit-IFP rings through group actions of units on nonzero nilpotent elements. We prove that if R is a unit-IFP ring such that there are finite number of orbits under the left (resp., right) action of units on nonzero nilpotent elements, then R satisfies the descending chain condition for nil left (resp., right) ideals of R and the upper nilradical of R is nilpotent.

• Bulletin of the Korean Chemical Society
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• v.28 no.10
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• pp.1715-1719
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• 2007

New bispsoralen derivatives 5-10, 8-MOP-NHCO(CH2)nCONH-8-MOP (BPSBA-Cn, n = 0, 1, 2, 3, 4 and 5) in which 5 position of an 8-methoxypsoralen (8-MOP) is linked by various lengths of bisamide polymethylene chain to 5 position of the other 8-MOP, have been synthesized by the amidation of 5-amino-8-methoxypsoralen (12) with α,ω-alkanoyl dichloride. Photophysical properties of their derivatives including π?π stacking interaction between the two aromatic moieties were investigated by UV absorption and fluorescence emission spectra. Efficient ring-ring stacking interactions have been observed in BPSBA-C4 (9) from the percent hypochromism (%H) of the models.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.57-64
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• 2020

Let R ⊆ T be an ascending chain of commutative rings with identity and H(R, T) (resp., h(R, T)) the composite Hurwitz series ring (resp., composite Hurwitz polynomial ring). In this article, we give some conditions for the rings H(R, T) and h(R, T) to be PS-rings.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.8
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• pp.2083-2100
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• 2023

The rise of Industry 5.0 has led to a smarter and more digital way of doing business, but with it comes the issue of user privacy and security. Only when privacy and security issues are addressed, will users be able to transact online with greater peace of mind. Thus, to address the security and privacy problems associated with industry blockchain technology, we propose a privacy protection scheme for online financial transactions based on verifiable ring signatures and blockchain by comparing and combining the unconditional anonymity provided by ring signatures with the high integrity provided by blockchain technology. Firstly, we present an algorithm for verifying ring signature based on distributed key generation, which can ensure the integrity of transaction data. Secondly, by using the block chain technique, we choose the proxy node to send the plaintext message into the block chain, and guarantee the security of the asset transaction. On this basis, the designed scheme is subjected to a security analysis to verify that it is completely anonymous, verifiable and unerasable. The protection of user privacy can be achieved while enabling online transactions. Finally, it is shown that the proposed method is more effective and practical than other similar solutions in performance assessment and simulation. It is proved that the scheme is a safe and efficient online financial transaction ring signature scheme.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.33-40
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• 2000

We prove some characterization of rings with chain conditions in terms of fuzzy quotient rings and fuzzy ideals. We also show that a ring R is left Artinian if and only of the set of values of every fuzzy ideal on R is upper well-ordered.

• Bulletin of the Korean Chemical Society
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• v.21 no.8
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• pp.774-778
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• 2000

A convenient total synthesis of a new 7-deoxyidarubicinone ivative21,the aglycon of the anticancer anti-biotic idarubicin analogue,is described.Keyfeatures of the synthesis are the Friedel-Crafts acylation and the functionalization of an A-ring si de chain. A synthon 14 for the A and B rings was prepared from intermediate 6 in five steps.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1117-1123
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• 2001

A ring is a DICC ring if every chain of right ideals in-dexed by the integers stabilizes to the left or to the right or to both sides. A counterexample is given to an assertion of karamzadeh and Motamedi that a transfinite power of the Jacobson radical of a right DICC ring is zero. we determine the behavior of the transfinite powers of the Jacobson radical relative to a torsion theory and consequently can obtain their correct behavior in the classical setting.