• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.543-552
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• 2017

Let R be a commutative ring with identity, and ${\phi}:{\mathfrak{I}}(R){\rightarrow}{\mathfrak{I}}(R){\cup}\{{\varnothing}\}$ be a function where ${\mathfrak{I}}(R)$ is the set of all ideals of R. Following [2], a proper ideal P of R is called a ${\phi}$-prime ideal if $x,y{\in}R$ with $xy{\in}P-{\phi}(P)$ implies $x{\in}P$ or $y{\in}P$. For an ideal I of R, we define the ${\phi}$-radical ${\sqrt[{\phi}]{I}}$ to be the intersection of all ${\phi}$-prime ideals of R containing I, and show that this notion inherits most of the essential properties of the usual notion of radical of an ideal. We also investigate when the set of all ${\phi}$-prime ideals of R, denoted $Spec_{\phi}(R)$, has a Zariski topology analogous to that of the prime spectrum Spec(R), and show that this topological space is Noetherian if and only if ${\phi}$-radical ideals of R satisfy the ascending chain condition.

• Proceedings of the KIEE Conference
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• 1998.07a
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• pp.107-109
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• 1998

This paper presents mechanical analysis of gas turbine generator (113MVA, $3{\phi}$, 2P, 0.9PF, F class, 3600rpm, 60Hz, 13.8kV, 4.72kA, Air-Cooling) field coil deformation. Rotor end coil deformation is only appeared on turbine end but collector end coil is normal. Expansion direction of end coil is tangential not axial. Deformation appears more severe at top turn. Retaining ling is expanded by centrifugal force of coil and itself. In case friction coefficient between coil top surface and retaining ring insulation inner surface is small, coil end length ${\ell}$ does not change. However, in case friction coefficient big condition, coil end is expanded ${\Delta}{\ell}$ due to start and stop. Deformation is assumed about 30mm by watching photograph inner surface of retaining ring is coated by Teflon at manufacturing condition. Usually Teflon coating insulation surface is small friction coefficient. It's value 0.08${\sim}$0.15. However it's value exceeds more than 0.297. Since top turn deformation appears. The distortion and subsequent failure have occurred because of the lack of a sufficient slip-plane between the top field coil conductors and the inside surface of the retaining ring insulation on the turbine end of the field-winding.