• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.23-26
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• 1995

Throughout this paper R will always denote an integral domain with the quotient field K. Let A denote the polynomial ring R[x], I be an ideal of $A, I_K = I \otimes_R K$ and $J = I_K \cap A$.

• Restorative Dentistry and Endodontics
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• v.13 no.1
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• pp.91-101
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• 1988

The purpose of this study was to evaluate Ultrasonic devices in root canal enlargement, about the effects on the canal shape and on the cutting ability beyond the curvature in curved canals. 180 resin blocks with $40^{\circ}$ curvature in apical third and 16mm long canal were made of epoxy resin and smooth broaches. These blocks were devided into six groups. According to the devices (ENAC$^{(R)}$, HARMOSONIC$^{(R)}$, Sonic Air MM 3000$^{(R)}$) and files (Zipperer file, H-file, Flexofile, K-file, Sharper file), five groups were instrumented one minute with # 15 files, then the enlarged size was measured. And # 20 files were used again in the same groups, then the enlarged size was measured. In control group, the time which was taken to enlarge the canal from # 15 to # 20 by hand technique was measured. The data was analyzed statistically. Then the enlarged shapes were evaluated in six groups with the stereomicroscope and recorded in ideal and non-ideal canal shape to compare the effects of ultrasonic devices on the canal shape. Only the ideal shaped canals were used in the study whether the cutting ability beyond the curvature in curved canals was, or not. The files with whole flutes, no flutes, and flutes in apical 5mm only were used. The weight differences of pre-and post-instrumentation by Sonic Air MM 3000$^{(R)}$ for two minutes were compared. The results were as follow: 1. Intracanal instrumentation for 1 minute with ultrasonic devices using # 15 and # 20 file in curved root canal of the epoxy resin block can not reach to the next file size. 2. Sonic Air MM 3000$^{(R)}$ shows higher cutting ability than the other two devices (p=0.001), however the percentage of non-ideal canal shape was the highest. 3. Two ultrasonic devices except Sonic Air MM 3000 considered normal in ideal canal shaping ability. 4. little cutting ability was shown beyond the curvature of curved canals.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.295-306
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• 2012

Let (R, $m_R$, k) be a local maximal commutative subalgebra of $M_n$(k) with nilpotent maximal ideal $m_R$. In this paper, we will construct a maximal commutative subalgebra $R^{ST}$ which is isomorphic to R and study some interesting properties related to $R^{ST}$. Moreover, we will introduce a method to construct an algebra in $MC_n$(k) with i($m_R$) = n and dim(R) = n.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.543-549
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• 2001

We show that R[X] is a Krull (Resp. factorial) ring if and only if R is a normal Krull (resp, factorial) ring with a finite number of minimal prime ideals if and only if R is a Krull (resp. factorial) ring with a finite number of minimal prime ideals and R(sub)M is an integral domain for every maximal ideal M of R. As a corollary, we have that if R[X] is a Krull (resp. factorial) ring and if D is a Krull (resp. factorial) overring of R, then D[X] is a Krull (resp. factorial) ring.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.789-794
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• 2007

Let R be a 3-torsion free semiprime ring and let I be a nonzero two-sided ideal of R. Suppose that there exists a permuting 3-derivation ${\Delta}:R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on I. Then the trace of ${\Delta}$ is commuting on I. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.101-106
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• 2006

Let R be a prime ring and I a nonzero ideal of R. Let $\alpha,\;\nu,\;\tau\;R{\rightarrow}R$ be the endomorphisms and $\beta,\;\mu\;R{\rightarrow}R$ the automorphisms. If R admits a generalized $(\alpha,\;\beta)-derivation$ g associated with a nonzero $(\alpha,\;\beta)-derivation\;\delta$ such that $g([\mu(x),y])\;=\;[\nu/(x),y]\alpha,\;\tau$ for all x, y ${\in}I$, then R is commutative.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.793-807
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• 2020

Stable range of rings is a unifying concept for problems related to the substitution and cancellation of modules. The newly appeared element-wise setting for the simplest case of stable range one is tempting to study the lifting property modulo ideals. We study the lifting of elements having (idempotent) stable range one from a quotient of a ring R modulo a two-sided ideal I by providing several examples and investigating the relations with other lifting properties, including lifting idempotents, lifting units, and lifting of von Neumann regular elements. In the case where the ring R is a left or a right duo ring, we show that stable range one elements lift modulo every two-sided ideal if and only if R is a ring with stable range one. Under a mild assumption, we further prove that the lifting of elements having idempotent stable range one implies the lifting of von Neumann regular elements.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.705-714
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• 2023

Bennis and El Hajoui have defined a (commutative unital) ring R to be S-coherent if each finitely generated ideal of R is a S-finitely presented R-module. Any coherent ring is an S-coherent ring. Several examples of S-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the S-coherent property to trivial ring extensions and amalgamated duplications.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.615-624
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• 1998

We consider a generalization of [1. theorem 2.5]. We give a description of the element of $_{\mathcal I}^l$(resp. $_{\mathcal I} ^r$), where A and B are left (resp. right)${\mathcal I}$-ideals of an IS-algebra X. For a nonempty left (resp. right) stable, we obtain a condition for $_{\mathcal I}^l$(resp. $_{\mathcal I}^l$) to be closed. We give a characterization of a closed $\mathcal I$-ideal in an IS-algebra, and show that in a finite IS-algebra, every $\mathcal I$-ideal is closed.

• East Asian mathematical journal
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• v.17 no.2
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• pp.275-286
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• 2001

In this paper, a skew polynomial ring $R[x;\alpha]$ of a ring R with a monomorphism $\alpha$ are investigated as follows: For a reduced ring R, assume that $\alpha(P){\subseteq}P$ for any minimal prime ideal P in R. Then (i) $R[x;\alpha]$ is a reduced ring, (ii) a ring R is Baer(resp. quasi-Baer, p.q.-Baer, a p.p.-ring) if and only if the skew polynomial ring $R[x;\alpha]$ is Baer(resp. quasi-Baer, p.q.-Baer, a p.p.-ring).