• 대한수학회지
• /
• 제56권5호
• /
• pp.1285-1307
• /
• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• Kyungpook Mathematical Journal
• /
• 제62권3호
• /
• pp.407-423
• /
• 2022

In this paper, we determine the structure of rings that have secondary representation (called representable rings) and give some characterizations of these rings. Also, we characterize Artinian rings in terms of representable rings. Then we introduce completely representable modules, modules every non-zero submodule of which have secondary representation, and give some necessary and sufficient conditions for a module to be completely representable. Finally, we define strongly representable modules and give some conditions under which representable module is strongly representable.

• 대한수학회보
• /
• 제58권4호
• /
• pp.837-851
• /
• 2021

Let R ⊆ L ⊆ S be ring extensions. Two star operations ${\ast}_1{\in}Star(R,S)$, ${\ast}_2{\in}Star(L,S)$ are said to be linked if whenever $A^{{\ast}_1}= R^{{\ast}_1}$ for some finitely generated S-regular R-submodule A of S, then $(AL)^{{\ast}_2}=L^{{\ast}_2}$. We study properties of linked star operations; especially when ${\ast}_1$ and ${\ast}_2$ are strict star operations. We introduce the notion of Prüfer star multiplication extension ($P{\ast}ME$) and we show that under appropriate conditions, if the extension R ⊆ S is $P{\ast}_1ME$ and ${\ast}_1$ is linked to ${\ast}_2$, then L ⊆ S is $P{\ast}_2ME$.

• 전력전자학회논문지
• /
• 제28권1호
• /
• pp.76-81
• /
• 2023

A new test circuit for an MMC-based valve HVDC power converter is proposed. The proposed scheme satisfies the required clauses from IEC-62501. The valve test current contains second harmonic component and DC offset as well as a fundamental component that is quite similar to the real operating arm current of MMC based HVDC power system. The structure of the proposed test circuit is simple compared to conventional test circuits. Furthermore, the power supply voltage rating of the proposed test circuit is reduced dramatically around 20% of the conventional scheme with the same current rating. The validity of the proposed test circuit is verified through simulation and experimental results.

• Kyungpook Mathematical Journal
• /
• 제63권1호
• /
• pp.29-36
• /
• 2023

Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that a finitely generated R-module M is Noetherian if and only if for every prime ideal 𝔭 of R with Ann(M) ⊆ 𝔭, there exists a finitely generated submodule N^𝔭 of M such that 𝔭M ⊆ N^𝔭 ⊆ M(𝔭), where M(𝔭) = {x ∈ M | sx ∈ 𝔭M for some s ∈ R \ 𝔭}. In this paper, we generalize the Parkash and Kour version of Cohen's theorem for Noetherian modules to S-Noetherian modules and w-Noetherian modules.

• 대한수학회보
• /
• 제59권2호
• /
• pp.453-468
• /
• 2022

In this article, we define a module M to be G^z-extending if and only if for each z-closed submodule X of M there exists a direct summand D of M such that X ∩ D is essential in both X and D. We investigate structural properties of G^z-extending modules and locate the implications between the other extending properties. We deal with decomposition theory as well as ring and module extensions for G^z-extending modules. We obtain that if a ring is right G^z-extending, then so is its essential overring. Also it is shown that the G^z-extending property is inherited by its rational hull. Furthermore it is provided some applications including matrix rings over a right G^z-extending ring.

• 전력전자학회:학술대회논문집
• /
• 전력전자학회 2020년도 전력전자학술대회
• /
• pp.322-323
• /
• 2020

본 논문에서는 전압형 HVDC MMC용 서브모듈을 시험하기 위해 개발된 3kV, 1000A급 서브모듈 시험장치 개발을 제시한다. 제안하는 시스템은 실제 전압형 MMC 서브모듈 운전환경과 동일한 조건의 전압 및 전류를 모의하기 위한 회로구조와 제어 방식을 적용하였다. 또한, 제안하는 시스템은 MMC의 이상적인 동작뿐만 아니라 운용 중 발생하는 전류왜곡을 모사하여 실 운전 상황을 동일하게 모의하고, 서브모듈의 스위칭 동작으로 인하여 발생하는 커패시터 전류의 불연속성을 3kV, 1000A급 서브모듈 시험장치 시작품을 통해 구현하였다. 또한, HILS로 구현된 전압형 HVDC MMC에서 서브모듈의 동작 특성과 비교하여 그 타당성을 검증하였다.

• 대한수학회보
• /
• 제60권4호
• /
• pp.971-983
• /
• 2023

In this paper, we prove that a domain R is an FGV-domain if every finitely generated torsion-free R-module is strongly copure projective, and a coherent domain is an FGV-domain if and only if every finitely generated torsion-free R-module is strongly copure projective. To do this, we characterize G-Prüfer domains by G-flat modules, and we prove that a domain is G-Prüfer if and only if every submodule of a projective module is G-flat. Also, we study the D + M construction of G-Prüfer domains. It is seen that there exists a non-integrally closed G-Prüfer domain that is neither Noetherian nor divisorial.

• 대한수학회보
• /
• 제20권1호
• /
• pp.45-49
• /
• 1983

If R is ring and M is a right (or left) R-module, then M is called a faithful R-module if, for some a in R, x.a=0 for all x.mem.M then a=0. In [4], R.E. Johnson defines that M is a prime module if every non-zero submodule of M is faithful. Let us define that M is of prime type provided that M is faithful if and only if every non-zero submodule is faithful. We call a right (left) ideal I of R is of prime type if R/I is of prime type as a R-module. This is equivalent to the condition that if xRy.subeq.I then either x.mem.I ro y.mem.I (see [5:3:1]). It is easy to see that in case R is a commutative ring then a right or left ideal of a prime type is just a prime ideal. We have defined in [5], that a chain of right ideals of prime type in a ring R is a finite strictly increasing sequence I$_{0}$.contnd.I$_{1}$.contnd....contnd.I$_{n}$; the length of the chain is n. By the right dimension of a ring R, which is denoted by dim, R, we mean the supremum of the length of all chains of right ideals of prime type in R. It is an integer .geq.0 or .inf.. The left dimension of R, which is denoted by dim$_{l}$ R is similarly defined. It was shown in [5], that dim$_{r}$R=0 if and only if dim$_{l}$ R=0 if and only if R modulo the prime radical is a strongly regular ring. By "a strongly regular ring", we mean that for every a in R there is x in R such that axa=a=a$^{2}$x. It was also shown that R is a simple ring if and only if every right ideal is of prime type if and only if every left ideal is of prime type. In case, R is a (right or left) primitive ring then dim$_{r}$R=n if and only if dim$_{l}$ R=n if and only if R.iden.D$_{n+1}$ , n+1 by n+1 matrix ring on a division ring D. in this paper, we establish the following results: (1) If R is prime ring and dim$_{r}$R=n then either R is a righe Ore domain such that every non-zero right ideal of a prime type contains a non-zero minimal prime ideal or the classical ring of ritght quotients is isomorphic to m*m matrix ring over a division ring where m.leq.n+1. (b) If R is prime ring and dim$_{r}$R=n then dim$_{l}$ R=n if dim$_{l}$ R=n if dim$_{l}$ R<.inf. (c) Let R be a principal right and left ideal domain. If dim$_{r}$R=1 then R is an unique factorization domain.TEX>R=1 then R is an unique factorization domain.

• 전력전자학회논문지
• /
• 제18권3호
• /
• pp.270-278
• /
• 2013

This paper proposes a control method for high voltage direct current(HVDC) with modular multilevel converter (MMC) under unbalanced voltage conditions considering the submodule(SM)'s current capacity and circulating current. It is aimed to propose a control method in which the current peak value does not exceed the maximum value of HVDC-MMC by considering the current capacity of the SM under unbalance voltage conditions. And it analyzes the effect of the unbalanced voltage on circulating currents in MMC and then proposes a control method considering each component of circulating currents under unbalanced voltages. The effectiveness of the proposed controlling method is verified through simulation results using PSCAD/EMTDC.