• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.577-586
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• 2000

For a grading monoid S, we prove that (1) if (S, M) is a valuation semigroup, then M is an m-canonical ideal, that is, an ideal M such that M : (M:J)=J for every ideal J of S. (2) if S is an integrally closed semigroup and S has a principal m-canonical ideal, then S is a valuation semigroup, and (3) if S is a completely integrally closed and S has an m-canonical ideal I, then every ideal of S is I-invertible, that is, J+(I+J)=I for every ideal J of S.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.555-565
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• 2014

An ideal I of a ring R is strongly ${\pi}$-regular if for any $x{\in}I$ there exist $n{\in}\mathbb{N}$ and $y{\in}I$ such that $x^n=x^{n+1}y$. We prove that every strongly ${\pi}$-regular ideal of a ring is a B-ideal. An ideal I is periodic provided that for any $x{\in}I$ there exist two distinct m, $n{\in}\mathbb{N}$ such that $x^m=x^n$. Furthermore, we prove that an ideal I of a ring R is periodic if and only if I is strongly ${\pi}$-regular and for any $u{\in}U(I)$, $u^{-1}{\in}\mathbb{Z}[u]$.

• 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.

• Journal of Magnetics
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• v.17 no.2
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• pp.145-152
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• 2012

Patients who underwent hip arthroplasty using the conventional fat suppression technique (CHESS) and a new technique (IDEAL) were compared quantitatively to assess the effectiveness and usefulness of the IDEAL technique. In 20 patients who underwent hip arthroplasty from March 2009 to December 2010, fat suppression T2 and T1 weighted images were obtained on a 3.0T MR scanner using the CHESS and IDEAL techniques. The level of distortion in the area of interest, the level of the development of susceptibility artifacts, and homogeneous fat suppression were analyzed from the acquired images. Quantitative analysis revealed the IDEAL technique to produce a lower level of image distortion caused by the development of susceptibility artifacts due to metal on the acquired images compared to the CHESS technique. Qualitative analysis of the anterior area revealed the IDEAL technique to generate fewer susceptibility artifacts than the CHESS technique but with homogeneous fat suppression. In the middle area, the IDEAL technique generated fewer susceptibility artifacts than the CHESS technique but with homogeneous fat suppression. In the posterior area, the IDEAL technique generated fewer susceptibility artifacts than the CHESS technique. Fat suppression was not statistically different, and the two techniques achieved homogeneous fat suppression. In conclusion, the IDEAL technique generated fewer susceptibility artifacts caused by metals and less image distortion than the CHESS technique. In addition, homogeneous fat suppression was feasible. In conclusion, the IDEAL technique generates high quality images, and can provide good information for diagnosis.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.535-546
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• 2011

Using $\mathcal{N}$-structures, the notion of an $\mathcal{N}$-ideal in a prelogic is introduced. Characterizations of an $\mathcal{N}$-ideal are discussed. Conditions for an $\mathcal{N}$-structure to be an $\mathcal{N}$-ideal are provided.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.379-390
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• 2008

More general forms of a BZ-ideal and a T-ideal are given, and appropriate examples are provided. The notion of T(m)-type BZ-algebra is introduced, and its characterizations are given.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.45-51
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• 2005

In this paper, we establish necessary and sufficient conditions for an exchange ideal to be a qb-ideal. It is shown that an exchange ideal I of a ring R is a qb-ideal if and only if when-ever $a{\simeq}b$ via I, there exists u ${\in} I_q^{-1}$ such that a = $ubu_q^{-1}$ and b = $u_q^{-1}$. This gives a generalization of the corresponding result of exchange QB-rings.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.173-184
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• 2010

Using $\cal{N}$-structures, the notion of an $\cal{N}$-ideal in a subtraction algebra is introduced. Characterizations of an $\cal{N}$-ideal are discussed. Conditions for an $\cal{N}$-structure to be an $\cal{N}$-ideal are provided. The description of a created $\cal{N}$-ideal is established.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.375-381
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• 2012

We introduce the concepts of ordered quasi-ideals, ordered bi-ideals in an ordered ternary semigroup and study their properties. Also regular ordered ternary semigroup is defined and several ideal-theoretical characterizations of the regular ordered ternary semigroups are furnished.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.331-340
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• 2023

In this paper, the concept of a maximal chain of ideals is introduced. Some properties of such chains are studied. We introduce some other concepts related to a maximal chain of ideals such as the n-maximal ideal, the maximal dimension of a ring S (M. dim(S)), the maximal depth of an ideal K of S (M.d(K)) and maximal height of an ideal K(M.d(K)).