• 한국정보통신학회논문지
• /
• 제17권7호
• /
• pp.1531-1537
• /
• 2013

ICT 생태계의 동인으로 전자정부는 기존의 PC 기반 e-Gov를 무선 기반 m-Gov로의 스마트 전자정부 형태 변화를 가져온다. 이에 따라 스마트 정부 구현을 위해서 m-Gov 서비스를 활성화 하고, 이를 위해 전략을 수립하여야 한다. 또한 전략수립에 따른 대응책과 전자정부가 나아가야 하는 정책적 과제를 제시할 필요가 있다. 이것이 정부의 혁신과 대국민 삶의 질을 향상시키는 것으로써 행정이념 추구의 궁극적인 목적이다. 따라서 본 논문에서 스마트 정부의 구현을 위해서 m-Gov의 전망으로 전자정부 서비스 활성화를 위한 전략수립과 대응책, 그리고 m-Gov의 정책 방향의 과제를 제시하였다.

• 대한수학회보
• /
• 제47권2호
• /
• pp.385-399
• /
• 2010

Let $\sigma$ be an endomorphism and I a $\sigma$-ideal of a ring R. Pearson and Stephenson called I a $\sigma$-semiprime ideal if whenever A is an ideal of R and m is an integer such that $A{\sigma}^t(A)\;{\subseteq}\;I$ for all $t\;{\geq}\;m$, then $A\;{\subseteq}\;I$, where $\sigma$ is an automorphism, and Hong et al. called I a $\sigma$-rigid ideal if $a{\sigma}(a)\;{\in}\;I$ implies a $a\;{\in}\;I$ for $a\;{\in}\;R$. Notice that R is called a $\sigma$-semiprime ring (resp., a $\sigma$-rigid ring) if the zero ideal of R is a $\sigma$-semiprime ideal (resp., a $\sigma$-rigid ideal). Every $\sigma$-rigid ideal is a $\sigma$-semiprime ideal for an automorphism $\sigma$, but the converse does not hold, in general. We, in this paper, introduce the quasi $\sigma$-rigidness of ideals and rings for an automorphism $\sigma$ which is in between the $\sigma$-rigidness and the $\sigma$-semiprimeness, and study their related properties. A number of connections between the quasi $\sigma$-rigidness of a ring R and one of the Ore extension $R[x;\;{\sigma},\;{\delta}]$ of R are also investigated. In particular, R is a (principally) quasi-Baer ring if and only if $R[x;\;{\sigma},\;{\delta}]$ is a (principally) quasi-Baer ring, when R is a quasi $\sigma$-rigid ring.

• 대한수학회지
• /
• 제47권3호
• /
• pp.483-494
• /
• 2010

Let R be a non-commutative prime ring and I a non-zero left ideal of R. Let U be the left Utumi quotient ring of R and C be the center of U and k, m, n, r fixed positive integers. If there exists a generalized derivation g of R such that $[g(x^m)x^n,\;x^r]_k\;=\;0$ for all x $\in$ I, then there exists a $\in$ U such that g(x) = xa for all x $\in$ R except when $R\;{\cong}\;=M_2$(GF(2)) and I[I, I] = 0.

• East Asian mathematical journal
• /
• 제27권1호
• /
• pp.75-82
• /
• 2011

In this paper, we will introduce the concept of fuzzy mulitplication module. We will define a new operation called a product on th family of all fuzzy submodules of a fuzzy mulitplication module. We will define a fuzzy subset of the idealization ring R+M and find some relations with the product of fuzzy submodules and product of fuzzy ideals of the idealization ring R+M. Some properties of weakly fuzzy prime submoduels and fuzzy prime submodules which are de ned by T.K.Mukherjee M.K.Sen and D.Roy will be introduced. We will investigate some properties of fuzzy prime submodules of a fuzzy multiplication module.

• 대한수학회논문집
• /
• 제35권4호
• /
• pp.1045-1056
• /
• 2020

Let R be a commutative ring with unity. The extension of annihilating-ideal graph of R, $^{\bar{\mathbb{AG}}}$(R), is the graph whose vertices are nonzero annihilating ideals of R and two distinct vertices I and J are adjacent if and only if there exist n, m ∈ ℕ such that IⁿJ^m = (0) with Iⁿ, J^m ≠ (0). First, we differentiate when 𝔸𝔾(R) and $^{\bar{\mathbb{AG}}}$(R) coincide. Then, we have characterized the diameter and the girth of $^{\bar{\mathbb{AG}}}$(R) when R is a finite direct products of rings. Moreover, we show that $^{\bar{\mathbb{AG}}}$(R) contains a cycle, if $^{\bar{\mathbb{AG}}}$(R) ≠ 𝔸𝔾(R).

• 대한수학회보
• /
• 제59권5호
• /
• pp.1177-1190
• /
• 2022

Let R be a commutative ring with identity. We call the ring R to be an almost quasi-coherent ring if for any finite set of elements α₁, …, α_p and a of R, there exists a positive integer m such that the ideals $\bigcap{_{i=1}^{p}}\;R{\alpha}^m_i$ and Ann_R(α^m) are finitely generated, and to be almost von Neumann regular rings if for any two elements a and b in R, there exists a positive integer n such that the ideal (αⁿ, bⁿ) is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.

• 대한수학회지
• /
• 제51권4호
• /
• pp.853-866
• /
• 2014

Constacyclic codes of length $p^s$ over $R=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m}$ are precisely the ideals of the ring $\frac{R[x]}{<x^{p^s}-1>}$. In this paper, we investigate constacyclic codes of length $p^s$ over R. The units of the ring R are of the forms ${\gamma}$, ${\alpha}+u{\beta}$, ${\alpha}+u{\beta}+u^2{\gamma}$ and ${\alpha}+u^2{\gamma}$, where ${\alpha}$, ${\beta}$ and ${\gamma}$ are nonzero elements of $\mathbb{F}_{p^m}$. We obtain the structures and Hamming distances of all (${\alpha}+u{\beta}$)-constacyclic codes and (${\alpha}+u{\beta}+u^2{\gamma}$)-constacyclic codes of length $p^s$ over R. Furthermore, we classify all cyclic codes of length $p^s$ over R, and by using the ring isomorphism we characterize ${\gamma}$-constacyclic codes of length $p^s$ over R.

• 대한수학회지
• /
• 제53권2호
• /
• pp.381-401
• /
• 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).

• 대한수학회보
• /
• 제55권1호
• /
• pp.311-317
• /
• 2018

Let (R, m) be a commutative Noetherian local ring and I be an ideal of R. In this paper it is shown that if cd(I, R) = t > 0 and the R-module $Hom_R(R/I,H^t_I(R))$ is finitely generated, then $$t={\sup}\{{\dim}{\widehat{\hat{R}_p}}/Q:p{\in}V(I{\hat{R}}),\;Q{\in}mAss{_{\widehat{\hat{R}_p}}}{\widehat{\hat{R}_p}}\;and\;p{\widehat{\hat{R}_p}}=Rad(I{\wideha{\hat{R}_p}}=Q)\}$$. Moreover, some other results concerning the cohomological dimension of ideals with respect to the rings extension $R{\subset}R[X]$ will be included.

• Kyungpook Mathematical Journal
• /
• 제19권2호
• /
• pp.205-211
• /
• 1979

In this paper we continue the study of formation radical (F-radical) classes initiated in [3]. Hereditary and stronger properties of F-radical classes are discussed by giving construction for lower hereditary, lower stronger and lower strongly hereditary F-radical classes containing a given class M. It is shown that the Baer F-radical B is the lower strongly hereditary F-radical class containing the class of all nilpotent ideals and it is the upper radical class with $\{(I,\;N){\mid}N{\in}C,\;N\;is\;prime\}{\subset}SB$ where SB denotes the semisimple F-radical class of B and C is an arbitrary but fixed class of homomorphically closed near-rings. The existence of a largest F-radical class contained in a given class is examined using the concept of complementary F-radical introduced by Scott [5].