• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.97-111
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• 2015

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

• Honam Mathematical Journal
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• v.27 no.3
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• pp.353-367
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• 2005

Some properties of the intuitionistic fuzzy (1, 2)-ideal is considered. Characterizations of an intuitionistic fuzzy (1, 2)-ideal are given. We show that every intuitionistic fuzzy (1, 2)-ideal in a group is constant. Using a chain of (1, 2)-ideals of a semigroup S, an intuitionistic fuzzy (1, 2)-ideal of S is established.

• Journal of Digital Contents Society
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• v.11 no.2
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• pp.217-224
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• 2010

The purpose of this study was to examine the usefulness of IDEAL technique in breast MRI by performing a quantitative comparative analysis in patients diagnosed with DCIS. On a 3.0T MR scanner, fat-suppressed T2-weighted images and T1-weighted images before and after contrast enhancement were obtained from 20 patients histologically diagnosed with ductal carcinoma in situ (DCIS). The findings from the quantitative image analysis are the following: 1) On T2-weighted images, SNR were not significantly different in the lesion area itself between the CHESS and IDEAL groups, while the IDEAL group showed higher SNR at the ductal area and fat area than the CHESS group. In addition, the CNR were higher for the IDEAL group in those regions. 2) On T1-weighted images before enhancement, SNR were not significantly different in the lesion area itself between the CHESS and IDEAL groups, while the IDEAL group showed higher SNR at the ductal area and fat area than the CHESS group. In addition, the CNR were higher for the IDEAL group in those regions. 3) On T1-weighted images after enhancement, SNR were not significantly different in the lesion area itself between the CHESS and IDEAL groups, while the IDEAL group showed higher SNR at the ductal area and fat area than the CHESS group.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.181-184
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• 2006

We prove the following results: (1) Let R be a strongly euclidean semiring. Then an ideal A of $R_{n{\times}n}$ is a partitioning ideal if and only if it is a subtractive ideal. (2) A monic ideal M of R[$x$], where R is a strongly euclidean semiring, is a partitioning ideal if and only if it is a subtractive ideal.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1069-1078
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• 2021

Let R be a commutative ring with identity. A proper ideal I of R is called 1-absorbing primary ([4]) if for all nonunit a, b, c ∈ R such that abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. The concept of 1-absorbing primary ideals in a polynomial ring, in a PID and in idealization of a module is studied. Moreover, we introduce weakly 1-absorbing primary ideals which are generalization of weakly prime ideals and 1-absorbing primary ideals. A proper ideal I of R is called weakly 1-absorbing primary if for all nonunit a, b, c ∈ R such that 0 ≠ abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. Some properties of weakly 1-absorbing primary ideals are investigated. For instance, weakly 1-absorbing primary ideals in decomposable rings are characterized. Among other things, it is proved that if I is a weakly 1-absorbing primary ideal of a ring R and 0 ≠ I₁I₂I₃ ⊆ I for some ideals I₁, I₂, I₃ of R such that I is free triple-zero with respect to I₁I₂I₃, then I₁I₂ ⊆ I or I₃ ⊆ I.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.117-122
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• 2010

In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced $m_1$-system and $m_2$-system in semiring. We have shown that if Q is an ideal in the semiring R and if M is an $m_2$-system of R such that $\overline{Q}{\bigcap}M={\emptyset}$ then there exists as 2-prime ideal P of R such that Q $\subseteq$ P with $P{\bigcap}M={\emptyset}$.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.43-52
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• 2003

The fuzzification of positive implicative hyper K-ideals in hyper K-algebras is considered, Relations between fuzzy positive implicative hyper K-ideal and fuzzy hyper K-ideal are given. Characterizations of fuzzy positive implicative hyper K-ideals are provided. Using a family of positive implicative hyper K-ideals we make a fuzzy positive implicative hyper K-ideal. Using the notion of a fuzzy positive implicative hyper K-ideal, a weak hyper K-ideal is established.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.559-573
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• 2006

In this Paper three different types of fuzzy Prime ideals are introduced. Condition is obtained for a fuzzy 2-prime ideal will have two elements in its range. It has been shown that A is fuzzy 2-prime ideal of the semiring R if and only if 1-A is a fuzzy $m_2-system$ in R.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.185-198
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• 2002

We Consider the fuzzification of sub-implicative ideals in BCI-algebras, and investigate some related properties. We give conditions for a fuzzy ideal to be a fuzzy sub-implicative ideal. we show that (1) every fuzzy sub-implicative ideal is a fuzzy ideal, but the converse is not true, (2) every fuzzy sub-implicative ideal is a fuzzy positive implicative ideal, but the converse is not true, and (3) every fuzzy p-ideal is a fuzzy sub-implicative ideal, but the converse is not true. Using a family of sub-implicative ideals of a BCI-algebra, we establish a fuzzy sub-implicative ideal, and using a level set of a fuzzy set in a BCI-algebra, we give a characterization of a fuzzy sub-implicative ideal.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.8
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• pp.445-452
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• 2014

In this paper, we define ideal autocorrelation property for balanced quaternary sequence with even period. We also prove that our definition is ideal autocorrelation property for balanced quaternary sequence with even period. Furthermore, we propose a generation method of quaternary sequence with ideal autocorrelation property of period $2{\times}(2^n-1)$ using a binary sequence with ideal autocorrelation of period $2^n-1$ and Gray mapping. We also derive the autocorrelation value distribution of the newly proposed quaternary sequence.