• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.247-261
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• 2010

An associative ring R with identity is called a clean ring if every element of R is the sum of a unit and an idempotent. In this paper, we introduce the concept of f-clean rings. We study various properties of f-clean rings. Let C = $\(\array{A\;V\\W\;B}\)$ be a Morita Context ring. We determine conditions under which the ring C is f-clean. Moreover, we introduce the concept of rings having many full elements. We investigate characterizations of this kind of rings and show that rings having many full elements are closed under matrix rings and Morita Context rings.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.57-71
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• 2019

Let R be an associative ring with identity, M a t.u.p. monoid with only one unit and ${\omega}:M{\rightarrow}End(R)$ a monoid homomorphism. Let R be a reversible, M-compatible ring and ${\alpha}=a_1g_1+{\cdots}+a_ng_n$ a non-zero element in skew monoid ring $R{\ast}M$. It is proved that if there exists a non-zero element ${\beta}=b_1h_1+{\cdots}+b_mh_m$ in $R{\ast}M$ with ${\alpha}{\beta}=c$ is a constant, then there exist $1{\leq}i_0{\leq}n$, $1{\leq}j_0{\leq}m$ such that $g_{i_0}=e=h_{j_0}$ and $a_{i_0}b_{j_0}=c$ and there exist elements a, $0{\neq}r$ in R with ${\alpha}r=ca$. As a consequence, it is proved that ${\alpha}{\in}R*M$ is unit if and only if there exists $1{\leq}i_0{\leq}n$ such that $g_{i_0}=e$, $a_{i_0}$ is unit and aj is nilpotent for each $j{\neq}i_0$, where R is a reversible or right duo ring. Furthermore, we determine the relation between clean and nil clean elements of R and those elements in skew monoid ring $R{\ast}M$, where R is a reversible or right duo ring.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.519-526
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• 2005

In this paper, we prove that every exchange ring can be characterized by potent elements. Also we extend [10, Theorem 3.1 and Theorem 4.1] to quasi-clean rings in which every element is a sum of a potent element and a unit.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.183-195
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• 2019

Let R be a commutative ring with unity. In this paper, we characterize the unit elements, the regular elements, the ${\pi}$-regular elements and the clean elements of zero-symmetric near-ring of polynomials $R_0[x]$, when $nil(R)^2=0$. Moreover, it is shown that the set of ${\pi}$-regular elements of $R_0[x]$ forms a semigroup. These results are somewhat surprising since, in contrast to the polynomial ring case, the near-ring of polynomials has substitution for its "multiplication" operation.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.6
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• pp.853-859
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• 2001

This paper describes the extended topological clean up procedures to improve the quality of unstructured triangular meshes. As a postprocessing step, topological improvement procedures are applied both for elements that are interior to the mesh and for elements connected to the boundary and then Laplacian-like smoothing is used by default. Previous clean up algorithms are limited to eliminate the nodes of degree 3,4,8,9,10 and pairs of nodes of degree 5. In this study, new clean up algorithms which minimize the triple connection structures combined with degree 5 and 7 (ie ; 5-7-5, 7-7-5, 7-5-7 etc) are added. The suggested algorithms are applied to two example meshes to demonstrate the effectiveness of the approach in improving element quality in a finite element mesh.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.117-124
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• 2020

In 2013, Diesl defined a nil clean ring as a ring of which all elements can be expressed as the sum of an idempotent and a nilpotent. Furthermore, in 2017, Y. Zhou, S. Sahinkaya, G. Tang studied nil clean group rings, finding both necessary condition and sufficient condition for a group ring to be a nil clean ring. We have proposed a necessary and sufficient condition for a group ring to be a uniquely nil clean ring. Additionally, we provided theorems for general nil clean group rings, and some examples of trivial-center groups of which group ring is not nil clean over any strongly nil clean rings.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.759-767
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• 2011

An element of a ring is called strongly nil clean provided that it can be written as the sum of an idempotent and a nilpotent element that commute. A ring is strongly nil clean in case each of its elements is strongly nil clean. We investigate, in this article, the strongly nil cleanness of 2${\times}$2 matrices over local rings. For commutative local rings, we characterize strongly nil cleanness in terms of solvability of quadratic equations. The strongly nil cleanness of a single triangular matrix is studied as well.

• STI Policy Review
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• v.1 no.3
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• pp.1-15
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• 2010

This paper makes the case that a new policy strategy to enhance a global green recovery is needed urgently. The new strategy requires two essential elements. First, G20 economies should follow the lead of South Korea and China and turn their green stimulus investments into a serious long-term commitment, and to support these investments, they should adopt environmental pricing policies and instigate pricing and regulatory reforms to reduce carbon dependency. Second, the G20 also needs to target and coordinate assistance to developing economies in science, technology and innovation (STI) for clean energy. Such assistance is essential to help developing economies to overcome the skills, technological and capital gap that they face in clean energy technologies over the long term. Reform of the Clean Development Mechanism (CDM) is also necessary to establish a long-term global price signal for carbon, and to increase the coverage of developing economies, the sectors and technologies and the overall financing of clean energy projects. Formulating such a policy strategy should appeal to both the Asian-Pacific and Western economies comprising the G20, and by working together to formulate such a strategy, the G20 could lead the way toward a new era of global economic management and STI cooperation in clean energy.

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2000.11a
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• pp.265-267
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• 2000

The objective of this study is to analyze, design and evaluate a new gas cleanup or sampling system that will remove erosive, corrosive, and fouling contaminants present in an effluent stream as either solid or liquid particles providing a clean gas stream. The gas clean-up or sampling system considered in this study is an irrigated, rotating element device. The device consists of a central disk-like hub from which emanate radially wires or cylindrical elements. (omitted)

• Journal of Physiology & Pathology in Korean Medicine
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• v.18 no.4
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• pp.1159-1162
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• 2004

We studied on the production of the ceramic by the mineral-Oriental medicine and the property of the clean active water depositting on the ceramic stone. The results are as follows: We properly mixed of maifanshi, mica, ochre, and added to a small amount cinnabar, and therefore formed the ceramic stone. By the plasticity process and the irradiating magnetic force recovered the disappeared a part of constitutent elements. The recovered effects were become higher the freshness, maintenance, deodoriztion, clean water. As well as having the ability on capture of the notoxious heavy metal on human. The ceramic powder were mixed proper dose maifanshi, mica. And the powder had ionization, absorption, adhesion by the plasticity process and magnetic force. The clean active water of depositting on the ceramic stone during 24hours were observed significant the content of micro element, dissolved oxygen, abstraction on Herbs.