• Title/Summary/Keyword: (1, 2)-ideal

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ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

  • Badawi, Ayman;Tekir, Unsal;Yetkin, Ece
    • 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.

INTUITIONISTIC FUZZY (1, 2)-IDEALS OF SEMIGROUPS

  • JUN, YOUNG BAE;ROH, EUN HWAN;SONG, SEOK ZUN
    • 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.

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Evaluation of Usefulness of IDEAL(Iterative decomposition of water and fat with echo asymmetry and least squares estimation) Technique in 3.0T Breast MRI (3.0T 자기공명영상을 이용한 유방 검사시 IDEAL기법의 유용성 평가)

  • Cho, Jae-Hwan
    • 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.

On Partitioning Ideals of Semirings

  • Gupta, Vishnu;Chaudhari, Jayprakash Ninu
    • 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.

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SOME RESULTS ON 1-ABSORBING PRIMARY AND WEAKLY 1-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

  • Nikandish, Reza;Nikmehr, Mohammad Javad;Yassine, Ali
    • 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.

1-(2-) Prime Ideals in Semirings

  • Nandakumar, Pandarinathan
    • 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 $P{\bigcap}M={\emptyset}$.

Fuzzy Positive Implicative Hyper K-ideals in Hyper K-algebras

  • Jun, Young Bae;Shim, Wook Hwan
    • 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.

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FUZZY SUB-IMPLICATIVE IDEALS OF BCI-ALGEBRAS

  • Jun, Young-Bae
    • 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.

Quaternary Sequence with Ideal Autocorrelation Property (이상적인 자기 상관 특성을 갖는 4진 수열)

  • Jang, Ji-Woong
    • 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.