• Kyungpook Mathematical Journal
• /
• v.51 no.1
• /
• pp.1-10
• /
• 2011

Let (R, T) be a normal pair of commutative rings (i.e., R ${\subseteq}$ T is a unita extension of commutative rings, not necessarily integral domains, such that S is integrally closed in T for each ring S such that R ${\subseteq}$ S ${\subseteq}$ T) such that the total quotient ring of R is a von Neumann regular ring. Let P be one of the following ring-theoretic properties: going-down ring, extensionally going-down (EGD) ring, locally divided ring. Then R has P if and only if T has P. An example shows that the "if" part of the assertion fails if P is taken to be the "divided domain" property.

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

• Communications of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.127-136
• /
• 2019

This article concerns the normal property of elements on Jacobson and nil radicals which are generalizations of commutativity. A ring is said to be right njr if it satisfies the normal property on the Jacobson radical. Similarly a ring is said to be right nunr (resp., right nlnr) if it satisfies the normal property on the upper (resp., lower) nilradical. We investigate the relations between right duo property and the normality on Jacobson (nil) radicals. Related examples are investigated in the procedure of studying the structures of right njr, nunr, and nlnr rings.

• Journal of the Korean Mathematical Society
• /
• v.60 no.3
• /
• pp.683-694
• /
• 2023

Let a be an ideal of 𝔞 commutative noetherian ring R. We give some descriptions of the 𝔞-depth of 𝔞-relative Cohen-Macaulay modules by cohomological dimensions, and study how relative Cohen-Macaulayness behaves under flat extensions. As applications, the perseverance of relative Cohen-Macaulayness in a polynomial ring, formal power series ring and completion are given.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.813-822
• /
• 2014

A ring R is called quasipolar if for every a 2 R there exists $p^2=p{\in}R$ such that $p{\in}comm^2{_R}(a)$, $ a+p{\in}U(R)$ and $ap{\in}R^{qnil}$. The class of quasipolar rings lies properly between the class of strongly ${\pi}$-regular rings and the class of strongly clean rings. In this paper, we determine when a $2{\times}2$ matrix over a local ring is quasipolar. Necessary and sufficient conditions for a $2{\times}2$ matrix ring to be quasipolar are obtained.

• Journal of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.821-841
• /
• 2022

In this paper, we introduce and study regular rings relative to the hereditary torsion theory w (a special case of a well-centered torsion theory over a commutative ring), called w-regular rings. We focus mainly on the w-regularity for w-coherent rings and w-Noetherian rings. In particular, it is shown that the w-coherent w-regular domains are exactly the Prüfer v-multiplication domains and that an integral domain is w-Noetherian and w-regular if and only if it is a Krull domain. We also prove the w-analogue of the global version of the Serre-Auslander-Buchsbaum Theorem. Among other things, we show that every w-Noetherian w-regular ring is the direct sum of a finite number of Krull domains. Finally, we obtain that the global weak w-projective dimension of a w-Noetherian ring is 0, 1, or ∞.

• Tribology and Lubricants
• /
• v.22 no.3
• /
• pp.119-126
• /
• 2006

In this paper, the contact behavior characteristics of a primary sealing components such as a seal ring and a seal seat has been presented for a small hydro-power turbine. Using the non-linear FEM analysis, the maximum temperature, the axial displacement, radial differences between a seal ring and a seal seat, and maximum contact normal stress have been analyzed for three optimized sealing profiles in which are designed based on the FEM analysis and Taguchi's experimental method. The three primary sealing profiles between a seal ring and a seal seat are strongly related to a leakage of a water for a hydro-power turbine and wear of a primary sealing component. The computed results show that the contact rubbing area between a seal ring and a seal seat is very important for reducing a friction heating and wear in a sealing gap, and increasing a contact normal stress in primary sealing components. Based on the FEM computation, models II and III in which have a small rubbing surface of seal rings show low dilatation of primary sealing components, and high normal contact stress between a seal ring and a seal seat. Thus, the FEM computed results recommend a short contacting width of a primary sealing component for reducing a leakage and thermal distortions, and expanding a seal life. This means that a conventional primary sealing component may be switched to a reduced sealing face of seal rings.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.29 no.2 s.233
• /
• pp.169-175
• /
• 2005

In this paper, the contact stress and strain distributions in elastomer O-ring seals have been analyzed using a non-linear finite element method. The stress behavior of PTFE materials is assumed as Odgen model because the sealing clearance between the flange and the surface of the O-ring is not small and the sealing pressure of working fluids covers from the atmospheric pressure to high pressure of 15MPa. The contact normal force and stress in wavy O-rings in which is developed for this analysis are uniformly distributed along the flange and the wall of the rectangular groove. And the normal sealing forces are also kept high compared to other contact sealing models such as the conventional O-ring and X-ring, Thus, the FEM computed results indicate that the sealing characteristic of wavy O-rings is food compared with other contact seals.

• Clinical and Experimental Pediatrics
• /
• v.46 no.3
• /
• pp.291-294
• /
• 2003

Ring chromosome 21 causes a multitude of phenotypes, ranging from severe abnormalities to normal. The proposed mechanism of ring formation, breakage of both short and long arms of a chromosome with subsequent end to end fusion, remains unproven. We encountered a 4-year-old boy who presented developmental delay, microcephaly, micrognathia, hypertelorism, low-set ears, mild optic nerve hypoplasia, cleft lip and palate, scoliosis and left foot valgus, but normal brain MRI. Chromosome study from peripheral blood showed 46,XY, r(21)(p11.2q22.1) karyotype. The authors report the first case of ring chromosome 21 in Korea with a review of the literature.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.837-849
• /
• 2018

In this paper, we study the closedness such as seminomality and t-closedness, and Noetherian-like properties such as piecewise Noetherianness and Noetherian spectrum, of Hurwitz polynomial rings and Hurwitz series rings. To do so, we construct an isomorphism between a Hurwitz polynomial ring (resp., a Hurwitz series ring) and a factor ring of a polynomial ring (resp., a power series ring) in a countably infinite number of indeterminates.