• Honam Mathematical Journal
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• v.38 no.2
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• pp.231-241
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• 2016

In this paper we will define the tight integral closure of a finite set of ideals of a ring relative to a module and we will study some related results.

• Honam Mathematical Journal
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• v.19 no.1
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• pp.47-52
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• 1997

• Honam Mathematical Journal
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• v.32 no.4
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• pp.675-687
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• 2010

In this paper the dual notion of tight closure of ideals relative to modules is introduced and some related results are obtained.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.475-483
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• 2017

In this paper we consider the tight closure of an ideal relative to a module whose its zero submodule has a primary decomposition.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.13-21
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• 1997

In recent years M. Hochster and C. Huneke introduced the notions of tight closure of an ideal and of the weak F-regularity of a ring of positive prime characteristic. Here 'F' stands for Frobenius. This notion enabled us to play an important role in a commutative ring theory, and other related topics.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.65-72
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• 1992

All rings are commutative, Noetherian with identity and of prime characteristic p, unless otherwise specified. First, we describe the definition of tight closure of an ideal and the properties about the tight closure used frequently. The technique used here for the tight closure was introduced by M. Hochster and C. Huneke [4,5, or 6]. Using the concepts of the tight closure and its properties, we will prove that if R is a complete local domain and F-rational, then R is Cohen-Macaulay. Next, we study the properties of R$^{+}$, the integral closure of a domain in an algebraic closure of its field of fractions. In fact, if R is a complete local domain of characteristic p>0, then R$^{+}$ is Cohen-Macaulay [8]. But we do not know this fact is true or not if the characteristic of R is zero. For the special case we can show that if R is a non-Cohen-Macaulay normal domain containing the rationals Q, then R$^{+}$ is not Cohen-Macaulay. Finally we will prove that if R is an excellent local domain of characteristic p and F-ratiional, then R is Cohen-Macaulay.aulay.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.127-135
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• 2015

We determine two-interval normalized tight frame wavelet sets for real dilation $d{\in}(1,{\infty})$, and characterize all symmetric normalized tight frame wavelet sets. We also construct a normalized tight frame wavelet set which has an infinite number of components accumulating at the origin. These normalized tight frame wavelet sets and their closures possess the same measure. Finally an example of a normalized tight frame wavelet set is provided whose measure is strictly less than the measure of its closure.

• Communications of the Korean Mathematical Society
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• v.4 no.2
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• pp.273-277
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• 1989

• Journal of Veterinary Clinics
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• v.39 no.6
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• pp.353-359
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• 2022

Several suture patterns can be used for cystotomy closure, and a continuous suture pattern is the most commonly used. In this study, the fluid-tight ability and other suitabilities of continuous appositional sutures, such as the simple continuous suture pattern (SC), running suture pattern (RN), and Ford interlocking suture pattern (FI), were compared for cystotomy closure. Cystotomy closure was performed using each suture method in 10 cases of ex vivo swine bladders in each group. Suture time, leakage site, suture length, bursting pressure (BP), bursting volume (BV), and circular bursting wall tension (CBWT) were measured. Suture time and suture length were the shortest in RN and the longest in FI. Leakage occurred in two places: the incision line directly and the hole made by the suture. Leakage occurred through the incision line in 4 bladders of the RN group and 2 bladders of the FI group, but not in the SC group, and in the rest of the bladders, leakage occurred through the suture hole. The values of BP, BV, and CBWT increased in the order of FI, SC, and RN. Suture time and suture length can be considered as factors related to healing and side effects. In this study, leakage through the incision was found in a less appositional area; therefore, leakage through the hole could be considered an indicator of better apposition. Good apposition is one of the conditions required for ideal cystotomy closure. The bursting strength representing the fluid-tight ability can be expressed as the CBWT. RN is expected to be efficient and cause a small degree of foreign body reaction; however, it is expected to be less stable. FI has the greatest fluid-tightness ability, but it has been proposed that side effects due to foreign body reactions most frequently occur in FI. In conclusion, SC, which is expected to have a sufficient degree of fluid-tightness and appropriate recovery, is preferable to other continuous appositional suturing methods for cystotomy closure.

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.175-180
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• 1991

In [3], [4] and [5], Hochster and Huneke introduced the notions of the tight closure of an ideal and of the weak F-regularity of a ring. This notion enabled us to give new proofs of many results in commutative algebra. A regular ring is known to be F-regular, and a Gorenstein local ring is proved to be F-regular provided that one ideal generated by a system of parameters (briefly s.o.p.) is tightly closed. In fact, a Gorenstein local ring is weakly F-regular if and only if there exists a system of parameters ideal which is tightly closed [3]. But we do not know whether this fact is true or not if a ring is not Gorenstein, in particular, a ring is a Cohen Macaulay (briefly C-M) local ring. In this paper, we will prove this in the case of an 1-dimensional C-M local ring. For this, we study the F-rationality and the normality of the ring. And we will also prove that a C-M local ring is to be Gorenstein under some additional condition about the tight closure.