• Korean Journal of Mathematics
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• v.21 no.1
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• pp.41-53
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• 2013

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto power-series rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of nil power-serieswise Armendariz rings. Finally, we study the nil-Armendariz property for Ore extensions and skew power series rings.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.405-416
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• 2011

In this paper, we first introduce the concept of left strongly simple po-semigroups, then we discuss properties and characterizations nil-extensions of left strongly simple po-semigroups and semilattices of leftstrongly simple po-semigroups. Finally, we give some characterizations of the chain of left strongly simple po-semigroups.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1251-1267
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• 2014

The semicommutative property of rings was introduced initially by Bell, and has done important roles in noncommutative ring theory. This concept was generalized to one of nil-semicommutative by Chen. We first study some basic properties of nil-semicommutative rings. We next investigate the structure of Ore extensions when upper nilradicals are ${\sigma}$-rigid ${\delta}$-ideals, examining the nil-semicommutative ring property of Ore extensions and skew power series rings, where ${\sigma}$ is a ring endomorphism and ${\delta}$ is a ${\sigma}$-derivation.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1095-1106
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• 2020

The purpose of this paper is to introduce a new class of rings that is closely related to the class of pseudo-Krull domains. Let 𝓗 = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. Let R ∈ 𝓗 be a ring with total quotient ring T(R) and define 𝜙 : T(R) → R_Nil(R) by ${\phi}({\frac{a}{b}})={\frac{a}{b}}$ for any a ∈ R and any regular element b of R. Then 𝜙 is a ring homomorphism from T(R) into R_Nil(R) and 𝜙 restricted to R is also a ring homomorphism from R into R_Nil(R) given by ${\phi}(x)={\frac{x}{1}}$ for every x ∈ R. We say that R is a 𝜙-pseudo-Krull ring if 𝜙(R) = ∩ R_i, where each R_i is a nonnil-Noetherian 𝜙-pseudo valuation overring of 𝜙(R) and for every non-nilpotent element x ∈ R, 𝜙(x) is a unit in all but finitely many R_i. We show that the theories of 𝜙-pseudo Krull rings resemble those of pseudo-Krull domains.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.649-661
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• 2015

Insertion-of-factors-property, which was introduced by Bell, has a role in the study of various sorts of zero-divisors in noncommutative rings. We in this note consider this property in the case that factors are restricted to maximal ideals. A ring is called IMIP when it satisfies such property. It is shown that the Dorroh extension of A by K is an IMIP ring if and only if A is an IFP ring without identity, where A is a nil algebra over a field K. The structure of an IMIP ring is studied in relation to various kinds of rings which have roles in noncommutative ring theory.

• The Research Journal of the Costume Culture
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• v.11 no.1
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• pp.118-134
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• 2003

The first purpose of this study is to take a better look it the background of Formalism art in the cultural society and to examine the aesthetic value of the formative arts of formalism architecture that are ail basically founded upon the study of Formalism. Secondly, it analyzes the aesthetic value of Formalism Art to Wear, Which can be explained as a mixture of art and fashion, by investigate to the features of art history. The results are as follows; First, Formalism Art to Wear of Simultaneity does not represent continuance but simultaneous. In other words. inside the same time and place of dimension, events art visualized without transformation. Secondly, formalism Art to Wear of Geometrical Aesthetics deals with a purely genuine atmosphere that pursues absolute perfection, composed abstract of geometrical shapes. Thirdly, Fomarlism Art to Wear of Deformation breaks analysis from balance and symmetry showing extreme transformation nil new vitality. Fourthly, Formalism Art to Wear of Space Extension experiments with post-corporeality. Post-corporeality centers the human body extension that is open to various boundaries of implosion and electronic technologies, providing us with a new Cyborg of the digital body.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1309-1325
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• 2016

This note focuses on a ring property in which upper and lower nilradicals coincide, as a generalizations of symmetric rings. The concept of symmetric ideal and ring in the noncommutative ring theory was initially introduced by Lambek, as an extension of the usual commutative ideal theory. The investigation of symmetric rings provided many useful results to the study in the noncommutative ring theory. So the results obtained from this study may be applicable to observing the structure of zero divisors in various kinds of algebraic systems containing matrix rings and polynomial rings.