• 대한수학회논문집
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• 제34권4호
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• pp.1069-1078
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• 2019

Let R be a ring with identity and P(R) denote the prime radical of R. An element r of a ring R is called strongly P-clean, if there exists an idempotent e such that $r-e=p{\in}P$(R) with ep = pe. In this paper, we determine necessary and sufficient conditions for an element of a trivial Morita context to be strongly P-clean.

• 대한수학회보
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• 제59권6호
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• pp.1557-1565
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• 2022

In this paper, Glift codes, generalized lifted polynomials, matrices are introduced. The advantage of Glift code is "distance preserving" over the ring R. Then optimal codes can be obtained over the rings by using Glift codes and lifted polynomials. Zero divisors are classified to satisfy "distance preserving" for codes over non-chain rings. Moreover, Glift codes apply on MDS codes and MDS codes are obtained over the ring 𝓡 and the non-chain ring 𝓡_e,s.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.437-453
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• 2022

Unlike for polynomial rings, the notion of multiplication for the near-ring of polynomials is the substitution operation. This leads to somewhat surprising results. Let S be an abelian left near-ring with identity. The relation ~ on S defined by letting a ~ b if and only if ann_S(a) = ann_S(b), is an equivalence relation. The compressed zero-divisor graph 𝚪_E(S) of S is the undirected graph whose vertices are the equivalence classes induced by ~ on S other than [0]_S and [1]_S, in which two distinct vertices [a]_S and [b]_S are adjacent if and only if ab = 0 or ba = 0. In this paper, we are interested in studying the compressed zero-divisor graphs of the zero-symmetric near-ring of polynomials R₀[x] and the near-ring of the power series R₀[[x]] over a commutative ring R. Also, we give a complete characterization of the diameter of these two graphs. It is natural to try to find the relationship between diam(𝚪_E(R₀[x])) and diam(𝚪_E(R₀[[x]])). As a corollary, it is shown that for a reduced ring R, diam(𝚪_E(R)) ≤ diam(𝚪_E(R₀[x])) ≤ diam(𝚪_E(R₀[[x]])).

• 대한수학회보
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• 제39권3호
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• pp.411-422
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• 2002

In this note we are concerned with relationships between one-sided ideals and two-sided ideals, and study the properties of polynomial rings whose maximal one-sided ideals are two-sided, in the viewpoint of the Nullstellensatz on noncommutative rings. Let R be a ring and R[x] be the polynomial ring over R with x the indeterminate. We show that eRe is right quasi-duo for $0{\neq}e^2=e{\in}R$ if R is right quasi-duo; R/J(R) is commutative with J(R) the Jacobson radical of R if R[$\chi$] is right quasi-duo, from which we may characterize polynomial rings whose maximal one-sided ideals are two-sided; if R[x] is right quasi-duo then the Jacobson radical of R[x] is N(R)[x] and so the $K\ddot{o}the's$ conjecture (i.e., the upper nilradical contains every nil left ideal) holds, where N(R) is the set of all nilpotent elements in R. Next we prove that if the polynomial rins R[x], over a reduced ring R with $\mid$X$\mid$ $\geq$ 2, is right quasi-duo, then R is commutative. Several counterexamples are included for the situations that occur naturally in the process of this note.

• 대한수학회지
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• 제58권1호
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• pp.149-171
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• 2021

Let Cl(A) denote the class group of an arbitrary integral domain A introduced by Bouvier in 1982. Then Cl(A) is the ideal class (resp., divisor class) group of A if A is a Dedekind or a Prüfer (resp., Krull) domain. Let G be an abelian group. In this paper, we show that there is a ring of Krull type D such that Cl(D) = G but D is not a Krull domain. We then use this ring to construct a Prüfer ring of Krull type E such that Cl(E) = G but E is not a Dedekind domain. This is a generalization of Claborn's result that every abelian group is the ideal class group of a Dedekind domain.

• 호남수학학술지
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• 제41권4호
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• pp.799-812
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• 2019

We introduce flat e-covers of modules and define e-perfect rings as a generalization of perfect rings. We prove that a ring is right perfect if and only if it is semilocal and right e-perfect which generalizes a result due to N. Ding and J. Chen. Moreover, in the light of the fact that a ring R is right perfect if and only if flat covers of any R-module are projective covers, we study on the rings over which flat covers of modules are (generalized) locally projective covers, and obtain some characterizations of (semi) perfect, A-perfect and B-perfect rings.

• 한국운동역학회지
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• 제12권2호
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• pp.65-75
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• 2002

본 연구는 리듬체조를 구성하는 기술 중에서 신체 기본요소군의 Jump에 포함되는 C난도 Ring jump의 3차원 동작분석을 통해 분석하여 선수들의 기술향상과 지도에 필요한 정량적 자료를 제공하는데 목적을 두었다. 이벤트별 소요시간에서는 E-3에서 0.409${\pm}$0.017sec로 가장 긴 소요시간을 보였다. 신체중심의 변위에서는 E-3에서 88.5${\pm}$1.3%로 가장 높은 높이를 보였다. 좌 우 발끝 속도에서는 E-2에서 각각 732.4${\pm}$46.1cm/sec, 1958.4${\pm}$25.1cm/sec로 가장 빠르게 나타났다. 상체후경각에서는 E-3에서 97.8degree로 가장 낮은 각도를 보였다. 슬관절 각변위에서는 E-3에서 좌 우 각각 92.8${\pm}$14.9degree, 69.2${\pm}$5.7degree로 가장 낮은 각도를 보였다. 족관절 각변위에서는 E-3에서 좌 우 각각 171.3${\pm}$6.9degree, 167.9${\pm}$8.4degree로 가장 큰 각도를 보였다. 이런 결과로 볼 때, Ring jump동작을 수행하기 위해서는 족관절의 신전을 통한 높은 점프로 상체를 후경할 수 있는 유연성과 체공을 시간을 갖추는 것이라고 사료된다.

• ETRI Journal
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• 제34권2호
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• pp.199-209
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• 2012

In transport networks, a multi-ring architecture is very useful to facilitate network planning and to design and provide more resilient services for customers. Unlike traditional synchronous optical network multi-rings, the service resiliency of Ethernet-based multi-rings is significantly impacted by the ring hierarchy because a link or node failure in a certain level ring triggers filtering database flush actions in all higher level rings as well as in the ring with the failure, and consequently a large amount of duplicated data frames may be flooded. In this paper, we investigate how the ring hierarchy impacts the service resiliency of multi-ring networks. Based on extensive experiments on various single- and multiple-link failures, we suggest two effective inter-ring connection rules to minimize the transient traffic and to ensure more resilient multi-ring networks. In addition, we consider a flush optimization technique called e-ADV, and show that the combination of e-ADV and multi-ring structures satisfying our inter-ring connection rules results in a more attractive survivability performance.

• 대한수학회지
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• 제38권5호
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• pp.915-935
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• 2001

Let V be any valuation domain and let E be a subset of the quotient field K of V. We study the ring of integer-valued polynomials on E, that is, Int(E, V)={f$\in$K[X]｜f(E)⊆V}. We show that, if E is precompact, then Int(E, V) has many properties similar to those of the classical ring Int(Z).In particular, Int(E, V) is dense in the ring of continuous functions C(E, V); each finitely generated ideal of Int(E, V) may be generated by two elements; and finally, Int(E, V) is a Prufer domain.

• 대한수학회보
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• 제37권3호
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• pp.429-435
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• 2000

Our main goal is to show that if there exist Jordan derivations D, E and G on a noncommutative 2-torsion free prime ring R such that$(G^2(x)+E(x))D(x)=0\ or\ D(x)(G^2(x)+E(x))=0\ for\ all\ x\inR$, then we have D=o or E=0, G=0.