• 대한수학회지
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• 제56권5호
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• pp.1403-1418
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• 2019

Let R be a commutative ring with unity. If f(x) is a zero-divisor polynomial such that $f(x)=c_f f_1(x)$ with $c_f{\in}R$ and $f_1(x)$ is not zero-divisor, then $c_f$ is called an annihilating content for f(x). In this case $Ann(f)=Ann(c_f )$. We defined EM-rings to be rings with every zero-divisor polynomial having annihilating content. We showed that the class of EM-rings includes integral domains, principal ideal rings, and PP-rings, while it is included in Armendariz rings, and rings having a.c. condition. Some properties of EM-rings are studied and the zero-divisor graphs ${\Gamma}(R)$ and ${\Gamma}(R[x])$ are related if R was an EM-ring. Some properties of annihilating contents for polynomials are extended to formal power series rings.

• 대한수학회보
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• 제20권1호
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• pp.45-49
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• 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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 학술회의 논문집 정보 및 제어부문 A
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• pp.75-78
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• 2003

In this paper, a second-order 3-bit DSM using DWA(Data Weighted Averaging) algorithm is designed for bluetooth Zero-IF Receiver. The designed circuit has two integrators using a designed OTA, nonoverlapping two-phase clerk generator, 3-bit A/D converter, DWA algorithm and 3-bit D/A converter An ideal model of second-order lowpass DSM with a 3-bit quantizer was configured by using MATLAB, and each coefficients and design specification of each blocks were determined to have 10-bit resolution in 1MHz channel bandwidth. The designed second-order 3-blt lowpass DSM has maximum SNR of 74dB and power consumption is 50mW at 3.3V.

• 대한수학회논문집
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• 제24권2호
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• pp.161-169
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• 2009

In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by $\widehat{{\Gamma}_I(N)}$. It is shown that if I is a completely reflexive ideal of N, then every two vertices in $\widehat{{\Gamma}_I(N)}$ are connected by a path of length at most 3, and if $\widehat{{\Gamma}_I(N)}$ contains a cycle, then the core K of $\widehat{{\Gamma}_I(N)}$ is a union of triangles and rectangles. We have shown that if $\widehat{{\Gamma}_I(N)}$ is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.

• 대한수학회지
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• 제53권2호
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• pp.381-401
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• 2016

According to Jacobson [31], a right ideal is bounded if it contains a non-zero ideal, and Faith [15] called a ring strongly right bounded if every non-zero right ideal is bounded. From [30], a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property (A) and the conditions asked by Nielsen [42]. It is shown that for a u.p.-monoid M and ${\sigma}:M{\rightarrow}End(R)$ a compatible monoid homomorphism, if R is reversible, then the skew monoid ring R * M is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and ${\sigma}:M{\rightarrow}End(R)$ is a weakly rigid monoid homomorphism, then the skew monoid ring R * M has right Property (A).

• 대한수학회지
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• 제47권5호
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• pp.1097-1106
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• 2010

Let R be a commutative ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will investigate some ring theoretic properties of R by considering $\Gamma$(R), the zero-divisor graph of R, under the regular action on X by G as follows: (1) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then there is a vertex of $\Gamma$(R) which is adjacent to every other vertex in $\Gamma$(R) if and only if R is a local ring or $R\;{\simeq}\;\mathbb{Z}_2\;{\times}\;F$ where F is a field; (2) If R is a local ring such that X is a union of n distinct orbits under the regular action of G on X, then all ideals of R consist of {{0}, J, $J^2$, $\ldots$, $J^n$, R} where J is the Jacobson radical of R; (3) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then the number of all ideals is finite and is greater than equal to the number of orbits.

• 한국정보통신학회논문지
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• 제8권4호
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• pp.879-885
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• 2004

본 논문에서는 DDC(Digital Down Convertor)를 가지는 디지털 수신기의 적응 신호처리에 대해 서술하였다. DDC는 NCO(Numerically Controlled Oscillator)와 디지털 LPF(Low Pass Filter)로 구성되어 있으며, 수치적 알고리즘에 의해 수신된 신호를 처리한다. 통과대역 샘플링 기법을 이용한 디지털 수신기의 시뮬레이션 결과를 보여주고 있으며, 수치적으로 처리되는 DDC에 의해 수신된 low IF 신호가 zero IF 신호로 변환되는 것을 확인하였다 또한, 고분해능을 가지는 MUSIC(Multiple Signal Classification) 알고리즘을 이용한 DOA(Direction Of Arrivals) 추정 기법을 기술하고 있다 DOA의 분해능의 정확도가 입력 샘플링 수와 안테나 소자 수에 의존하는 것을 확인하였다

• 대한수학회논문집
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• 제33권2호
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• pp.379-395
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• 2018

Assume that R is a commutative ring with non-zero identity which is not an integral domain. An ideal I of R is called an annihilating ideal if there exists a non-zero element $a{\in}R$ such that Ia = 0. S. Visweswaran and H. D. Patel associated a graph with the set of all non-zero annihilating ideals of R, denoted by ${\Omega}(R)$, as the graph with the vertex-set $A(R)^*$, the set of all non-zero annihilating ideals of R, and two distinct vertices I and J are adjacent if I + J is an annihilating ideal. In this paper, we study the relations between the diameters of ${\Omega}(R)$ and ${\Omega}(R[x])$. Also, we study the relations between the diameters of ${\Omega}(R)$ and ${\Omega}(R[[x]])$, whenever R is a Noetherian ring. In addition, we investigate the relations between the diameters of this graph and the zero-divisor graph. Moreover, we study some combinatorial properties of ${\Omega}(R)$ such as domination number and independence number. Furthermore, we study the complement of this graph.

• 대한수학회지
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• 제53권3호
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• pp.519-532
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• 2016

The zero-divisor graph of a noncommutative ring R, denoted by ${\Gamma}(R)$, is a graph whose vertices are nonzero zero-divisors of R, and there is a directed edge from a vertex x to a distinct vertex y if and only if xy = 0. Let $R=M_2(F_q)$ be the $2{\times}2$ matrix ring over a finite field $F_q$. In this article, we investigate the automorphism group of ${\Gamma}(R)$.

• 대한전자공학회논문지SD
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• 제47권2호
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• pp.100-105
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• 2010

본 논문에서는 Zero-Crossing 복조기에 적합한 88MHz에서 108MHz 대역 FM 라디오 수신기를 $0.5{\mu}m$ CMOS 공정을 이용하여 설계 및 제작하였다. 본 수신기는 Low-IF 구조를 기초로 설계되었으며, Low-Noise Amplifier (LNA), Down-Conversion Mixer, Phase locked loop (PLL), Low-pass filter (LPF), 비교기를 포함하는 RF/Analog 집적회로로 개발되었다. 측정결과 LNA와 Mixer를 포함하는 RF Block은 23.2dB의 변환 이득과 입력 PldB는 -14dBm였고 전체 잡음지수는 15 dB로 나타났다. IF단 LPF와 비교기를 포함하는 Analog Block은 89dB 이상의 전압 이득을 가지고, IC내부의 레지스터를 제어하여 600KHz에서 1.3MHz까지 100KHz 단위로 Passband 대역를 조절할 수 있도록 설계되었다. 설계된 수신기는 4.5V에서 동작하며, 전체 전류 소모는 15.3 mA로 68.85mW의 전력을 소모한다. 실험결과 성공적으로 FM 라디오 신호를 수신할 수 있었다.