• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.209-227
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• 2021

In this paper, we deal with the question that what kind of properties does a ring gain when it satisfies symmetricity or reversibility by the way of nilpotent elements? By the motivation of this question, we approach to symmetric and reversible property of rings via nilpotents. For symmetricity, we call a ring R middle right-(resp. left-)nil symmetric (mr-nil (resp. ml-nil) symmetric, for short) if abc = 0 implies acb = 0 (resp. bac = 0) for a, c ∈ R and b ∈ nil(R) where nil(R) is the set of all nilpotent elements of R. It is proved that mr-nil symmetric rings are abelian and so directly finite. We show that the class of mr-nil symmetric rings strictly lies between the classes of symmetric rings and weak right nil-symmetric rings. For reversibility, we introduce left (resp. right) N-reversible ideal I of a ring R if for any a ∈ nil(R), b ∈ R, being ab ∈ I implies ba ∈ I (resp. b ∈ nil(R), a ∈ R, being ab ∈ I implies ba ∈ I). A ring R is called left (resp. right) N-reversible if the zero ideal is left (resp. right) N-reversible. Left N-reversibility is a generalization of mr-nil symmetricity. We exactly determine the place of the class of left N-reversible rings which is placed between the classes of reversible rings and CNZ rings. We also obtain that every left N-reversible ring is nil-Armendariz. It is observed that the polynomial ring over a left N-reversible Armendariz ring is also left N-reversible.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.561-573
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• 2015

The aim of this paper is to introduce the notion of left-right (resp. right-left) symmetric bi-derivation of BCH-algebras and some related properties are investigated.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.777-788
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• 2007

An endomorphism ${\alpha}$ of a ring R is called right(left) symmetric if whenever abc=0 for a, b, c ${\in}$ R, $ac{\alpha}(b)=0({\alpha}(b)ac=0)$. A ring R is called right(left) ${\alpha}-symmetric$ if there exists a right(left) symmetric endomorphism ${\alpha}$ of R. The notion of an ${\alpha}-symmetric$ ring is a generalization of ${\alpha}-rigid$ rings as well as an extension of symmetric rings. We study characterizations of ${\alpha}-symmetric$ rings and their related properties including extensions. The relationship between ${\alpha}-symmetric$ rings and(extended) Armendariz rings is also investigated, consequently several known results relating to ${\alpha}-rigid$ and symmetric rings can be obtained as corollaries of our results.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.489-501
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• 2015

We study the structure of right duo ring property when it is restricted within the group of units, and introduce the concept of right unit-duo. This newly introduced property is first observed to be not left-right symmetric, and we examine several conditions to ensure the symmetry. Right unit-duo rings are next proved to be Abelian, by help of which the class of noncommutative right unit-duo rings of minimal order is completely determined up to isomorphism. We also investigate some properties of right unit-duo rings which are concerned with annihilating conditions.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.131-136
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• 2010

Throught this paper, we will investigate some properties of left regular and strongly reduced near-rings. Mason introduced the notion of left regularity and he characterized left regular zero-symmetric unital near-rings. Also, this concept have been studied by several authors. The purpose of this paper is to find some characterizations of the strong reducibility in near-rings, and the strong regularity in near-rings which are closely related with strongly reduced near-rings.

• Journal of Advanced Navigation Technology
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• v.17 no.2
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• pp.196-201
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• 2013

In this paper, a dual-mode balanced filter with symmetric coupled composite right/left-handed transmission line is introduced. Unlike the other symmetric structure, this configuration has the ability to operate under both common- and differential-mode excitation. These properties are achievable through providing physical short circuit by means of ground vias at the center of each unit-cell along the symmetry plane of the structure. Because the CRLH unit-cells are operated under both common- and differential-mode excitation, we implemented a balanced filter using these properties. To validity these features, a five-cell four port coupled CRLH-TL is simulated, fabricated and measured and the obtained performances agree with the simulation results under both common- and differential-mode excitation.

• Journal of the Korean Society of Visualization
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• v.11 no.1
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• pp.48-52
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• 2013

This paper presents experimental observation of asymmetric electrohydrodynamic flow generated around a pair of symmetric coplanar electrodes. Electrodes are attached on the bottom of the cavity containing a dielectric liquid, i.e., a mixture of dodecane and 0.5% wt Span80. In the first experiment, an AC voltage of 1500 V is applied with the frequency varying in the range 10~500 hz and the left electrode being grounded. The flow patterns show that the center line of vortices is unexpectedly tilted to the left side. If the right side electrode is grounded, the center line is tilted to the right side. The magnitude of the fluid velocity shows an irregular variation with the frequency in the range 10 Hz~100 Hz, beyond which it simply decays. In the second experiment, we applied fixed AC with 1000 V and 60 Hz superposed by DC voltage varying in the range -1000 V ~ +1000 V. The center line of the flow pattern is tilted to the right side with positive DC voltage and to the left side with negative DC. We have managed to show that the flow pattern can be symmetric with a suitable combination of DC and AC, e.g., DC 850 V plus AC 1000 V with the frequency 10 Hz.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.25-40
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• 2018

We focus on the structure of the set of noncentral idempotents whose role is similar to one of central idempotents. We introduce the concept of quasi-Abelian rings which unit-regular rings satisfy. We first observe that the class of quasi-Abelian rings is seated between Abelian and direct finiteness. It is proved that a regular ring is directly finite if and only if it is quasi-Abelian. It is also shown that quasi-Abelian property is not left-right symmetric, but left-right symmetric when a given ring has an involution. Quasi-Abelian property is shown to do not pass to polynomial rings, comparing with Abelian property passing to polynomial rings.

• Journal of Korean Physical Therapy Science
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• v.15 no.4
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• pp.11-17
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• 2008

Background: Human body is formed of symmetric bilateral structures that are comprised of eye, upper arm, lower arm and etc. but, we are used only dominant components. The purpose of this study was to analysis length cognition ability in dominant eye. Methods: Total 88 persons (male 18, female 70) were participated in this study. They were tested with ‘hole in the card’ test for identification of dominant eye's side, then the length cognition ability was measured in right & left axillary level by describing 10cm line. Results: The results by independent t-test were as follows. In difference of length cognition ability in right axillary level between right dominant eyed group & left dominant eyed group, right dominant eyed group was superior to left dominant eyed group, but significant difference was not existed statistically(p>.05). In left axillary level, right dominant eyed group was superior to left dominant eyed group, but significant difference was not existed statistically(p>.05). Conclusion: These result can be applied to the learning of palpation & observation skill in physical therapy, although this study was not identify a relation between dominant eye & dominant hand.

• Journal of Korean Physical Therapy Science
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• v.16 no.4
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• pp.59-65
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• 2009

Background: Human body is formed of symmetric bilateral structures that are comprised of eye, upper arm, lower arm and etc. but, we are used only dominant components. The purpose of this study was to analysis length cognition ability in dominant eye & hand. Method: Total 180 persons (male 32, female 138) were participated in this study. They were tested with 'hole in the card' test for identification of dominant eye's side and the question for identification of dominant hand's side, then the length cognition ability was measured in right & left axillary level by describing 10cm line. Results: The results by independent t-test were as follows. In difference of length cognition ability in right axillary level between right dominant eyed group & left dominant eyed group, right dominant eyed group was superior to left dominant eyed group, but significant difference was not existed statistically(p>.05). In left axillary level, right dominant eyed group was superior to left dominant eyed group, but significant difference was not existed statistically(p>.05). In axillary level of dominant eye's side, non-crossed group was superior to crossed group, but significant difference was not existed statistically(p>.05). In axillary level of non-dominant eye's side, non-crossed group was superior to crossed group, but significant difference was not existed statistically(p>.05). Conclusion: These result can be applied to the learning of palpation & observation skill in physical therapy.