• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.221-227
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• 2002

In this paper we will show that the followings ; (1) Let R be a regular local ring of dimension n. Then $A_{n-2}$(R) = 0. (2) Let R be a regular local ring of dimension n and I be an ideal in R of height 3 such that R/I is a Gorenstein ring. Then [I] = 0 in $A_{n-3}$(R). (3) Let R = V[[ $X_1$, $X_2$, …, $X_{5}$ ]]/(p+ $X_1$$^{t1}$ + $X_2$$^{t2}$ + $X_3$$^{t3}$ + $X_4$$^2$+ $X_{5}$ $^2$/), where p $\neq$2, $t_1$, $t_2$, $t_3$ are arbitrary positive integers and V is a complete discrete valuation ring with (p) = mv. Assume that R/m is algebraically closed. Then all the Chow group for R is 0 except the last Chow group.group.oup.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.399-404
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• 2005

Let M be a finite commutative nilpotent algebra over a perfect field k of prime characteristic p and let $M^p$ be the sub-algebra of M generated by $x^p$, $x{\in}M$. Eggert[3] conjectures that $dim_kM{\geq}pdim_kM^p$. In this paper, we show that the conjecture holds for $M=R^+/I$, where $R=k[X_1,\;X_2,\;{\cdots},\;X_t]$ is a polynomial ring with indeterminates $X_1,\;X_2,\;{\cdots},\;X_t$ over k and $R^+$ is the maximal ideal of R generated by $X_1,\;X_2,{\cdots},\;X_t$ and I is a monomial ideal of R containing $X_1^{n_1+1},\;X_2^{n_2+1},\;{\cdots},\;X_t^{n_t+1}$ ($n_i{\geq}0$ for all i).

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-10
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• 2021

Let R and S be two commutative rings, J be an ideal of S and f : R → S be a ring homomorphism. The amalgamation of R and S along J with respect to f, denoted by R ⋈f J, is the special subring of R × S defined by R ⋈f J = {(a, f(a) + j) | a ∈ R, j ∈ J}. In this paper, we study some basic properties of a special kind of R ⋈f J-modules, called the amalgamation of M and N along J with respect to ��, and defined by M ⋈�� JN := {(m, ��(m) + n) | m ∈ M and n ∈ JN}, where �� : M → N is an R-module homomorphism. The new results generalize some known results on the amalgamation of rings and the duplication of a module along an ideal.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.289-295
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• 2000

In this note, we define a ${Q^*}-ideal$ in a seminear-ring which is analogous of a Q-ideal in a semiring, and we construct a quotient seminear-ring. Also, We prove the fundamental theorem of homomorphisms for seminear-rings.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.243-250
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• 2003

The fuzzification of (Positive implicative) pseudo-ideals in a pseudo-BCK algebra is discussed, and several properties are investigated. Characterizations of a fuzzy pseudo-ideal are displayed.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1163-1173
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• 2014

Let R be a commutative ring with $1{\neq}0$. In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever $a,b,c{\in}R$ and $abc{\in}I$, then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sqrt{I}$. A number of results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are given.

• Membrane Journal
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• v.24 no.6
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• pp.491-497
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• 2014

PTMSP-silica composite membranes were prepared by addition of 0, 15, 20, and 30 wt% TEOS (tetraethoxysilane), TMOS (tetramethoxysilane), MTMOS (methyltrimethoxysilane), and PTMOS (phenyltrimethoxysilane) contents to PTMSP using sol-gel process. The gas permeability of the composite membranes for $H_2$, $N_2$ and ideal selectivity for $H_2$ over $N_2$ were investigated as a function of alkoxysilane content. The permeabilities for $H_2$ and $N_2$ increased in the range of alkoxysilane contents 0~20 wt%, however decrease the range of 20~30 wt%. The ideal selectivities for $H_2$ over $N_2$ decreased in the range of TEOS and PTMOS contents 0~15 wt%, but increased in the range of 15~30 wt%. When compared to the upper bound of Robeson, PTMSP-silica composite membranes with TEOS content of 30 wt%, MTMOS content of 20 wt% and PTMOS content of 30 wt% turned out to be a simultaneous improvement in ideal selectivity and permeability.

• Journal of architectural history
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• v.5 no.1 s.9
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• pp.87-101
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• 1996

This study aims at showing how C.N.Ledoux applied architecturally the idea of Enlightenment in the Ideal City. Enlightenment of 18th century not only developed neo-classicism in the field of art, but also brought about the changes of ideology and philosophy of the era. C.N.Ledoux, one of the most influential architects of this period, expressed abstractly and symbolically the essential idea of Enlightenment; the skepticism of God's authority, the liberty and equality of man, charity and the willingness of controlling the power of nature, and so on.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.887-893
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• 1996

Let (R,m) be a Cohen-Macaulay local ring with an infinite residue field and let $J = (a_1, \cdots, a_l)$ be a minimal reduction of an equimultiple ideal I of R. In this paper we shall prove that the following conditions are equivalent: (1) $I^2 = JI$. (2) $gr_I(R)/mgr_I(R)$ is Cohen-Macaulay with minimal multiplicity at its maximal homogeneous ideal N. (3) $N^2 = (a'_1, \cdots, a'_l)N$, where $a'_i$ denotes the images of $a_i$ in I/mI for $i = 1, \cdots, l$.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.683-687
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• 1998

Suppose X is a subspace of $(\sum_{n=1} ^{\infty} X_n)_{c_0}$, dim $X_n<{\infty}$, which has the metric compact approximation property. It is proved that if Y is a Banach space of cotype q for some $2{\leq}1<{\infty}$ then K(X,Y) is an M-ideal in L(X,Y).