• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.505-514
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• 2019

Let R be a commutative ring with identity and M be a unitary R-module. A submodule N of M is called a dense submodule if $Hom_R(M/N,\;E_R(M))=0$, where $E_R(M)$ is the injective hull of M. The R-module M is said to be monoform if any nonzero submodule of M is a dense submodule. In this paper, among the other results, it is shown that any kind of the following module is monoform. (1) The prime R-module M such that for any nonzero submodule N of M, $Ann_R(M/N){\neq}Ann_R(M)$. (2) Strongly prime R-module. (3) Faithful multiplication module over an integral domain.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1153-1167
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• 2005

In this paper, all rings and all near-rings R are associative, all modules are right R-modules. For a near-ring R, we consider representations of R as R-groups. We start with a study of AGR rings and their properties. Next, for any right R-module M, we define a new concept GM module and investigate the commutative property of faithful GM modules and some characterizations of GM modules. Similarly, for any near-ring R, we introduce an R-group with MR-property and some properties of MR groups.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.275-296
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• 2017

All rings considered here are commutative rings with identity and all modules considered here are unital left modules. A submodule N of an R-module M is said to be extended to M if $N=aM$ for some ideal a of R and it is said to be fully invariant if ${\varphi}(L){\subseteq}L$ for every ${\varphi}{\in}End(M)$. An R-module M is called a [resp., fully invariant] multiplication module if every [resp., fully invariant] submodule is extended to M. The class of fully invariant multiplication modules is bigger than the class of multiplication modules. We deal with prime submodules and associated prime submodules of fully invariant multiplication modules. In particular, when M is a nonzero faithful multiplication module over a Noetherian ring, we characterize the zero-divisors of M in terms of the associated prime submodules, and we show that the set Aps(M) of associated prime submodules of M determines the set $Zdv_M(M)$ of zero-dvisors of M and the support Supp(M) of M.

• The Journal of the Korea Contents Association
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• v.10 no.8
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• pp.59-65
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• 2010

This paper proposes an implementation of a hardware module for transmitting MPEG-2 TS data over the internet protocol (IP)-based network. This implementation consists of two modules; one is an encapsulation module which bridges between n TS packets, where $1\;{\leq}\;n\;{\leq}\;7$, and an IP packets, the other is a packet conversion module which extracts an DSM-CC PS packet from consecutive TS packets and then reconstructing an IP packet. So, these IP packets are carried over 150 megabits per second. Although overall work flow of the proposed DeMUX is based on the reference design of ALTERA, the DeMUX is enhanced by modifying it and performs more functions by adding a packet conversion module. The DeMUX is described by Verilog-HDL (hardware description language) and shows the faithful functionality and throughput through the simulation.

• Journal of IKEEE
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• v.4 no.2 s.7
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• pp.212-224
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• 2000

In this paper, a parallel processing system is proposed for improving the processing speed of image related applications. The proposed parallel processing system is fully synchronous SIMD computer with pipelined architecture and consists of processing elements and a multi-access memory system. The multi-access memory system is made up of memory modules and a memory controller, which consists of memory module selection module, data routing module, and address calculating and routing module, to perform parallel memory accesses with the variety of types: block, horizontal, and vertical access way. Morphological filter had been applied to verify the parallel processing system and resulted in faithful processing speed.

• The Journal of the Korea Contents Association
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• v.9 no.2
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• pp.60-66
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• 2009

In this paper, implementation of an ensemble transport interface (ETI) adapter for multimedia services based on terrestrial-digital multimedia broadcasting (T-DMB) is introduced. In general, ETI adapter should manipulate three functions: receiving packets packing multimedia data from service providers, configuring an ETI frame (G.703) from these data, and transmitting these frames to T-DMB multiplexer. To achieve these roles, the proposed ETI adapter consists of the network management module for data transmission and flow control between service providers and this adapter, the ETI configuration module for gathering data and then making ETI frames, and the hardware board for pushing ETI frames in real-time. The proposed adapter yielded faithful results without data lose on transmitting ETI frames to T-DMB multiplexer in the range of $64{\sim}1,153kbps$ specified in ETSI EN 300 401 after packing multimedia data received via Internet.

• Journal of architectural history
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• v.31 no.2
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• pp.27-34
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• 2022

This study aimed to elucidate the architectural characteristics of the cathedral architecture of the Archdiocese of Gwangju, which was completed in the period of liberation and turbulence, and the conclusions are as follows. Gwangju Archdiocese Cathedral, completed during the period of liberation and turbulence, was built with some assistance from the U.S. military or with the efforts of the faithful, and there are a number of factors such as space directing by Aps, the development of a simplified bell tower, the appearance of a stone cathedral, the application of a quenset structure, and an increase in size. show special features The indented apse appears only after liberation, and is a characteristic that appears prominently in stone churches. The simplified form in which the bell was hung by raising the outer wall appeared in the early church shows a change in the composition with a porch in front. The stone church and the quanset-structured church only appeared after liberation and were built only in the 1950s. The size of the cathedral reflects the increase in the number of believers after the Korean War, and the average area is about 1.5 times higher than before liberation. When considering the spacing of the bays as a module, the size plan followed the implicit norm of early cathedral architecture of 36.5m, but gradually decreased to 2.7m and 2.4m.