1985
DOI: 10.3836/tjm/1270151225
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On Stable Ideals

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Cited by 3 publications
(6 citation statements)
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“…(i) The "soft state" ULXs have inner disk temperatures Tin which are too high for their implied high masses. Equivalently, when the BH mass is estimated from the Eddington argument, Rin with reasonable correction for a boundary condition (Kubota et al 1998) and spectral hardening factor (Shimura & Takahara 1995) falls much below the last stable orbit for a non-spinning BH, 6Rg, where Rg = GM/c 2 is the gravitational radius. This contrasts with soft-state BHBs, where Rin generally agrees with 6Rg.…”
Section: A Comparison Of the Ulx With Bhbmentioning
confidence: 99%
“…(i) The "soft state" ULXs have inner disk temperatures Tin which are too high for their implied high masses. Equivalently, when the BH mass is estimated from the Eddington argument, Rin with reasonable correction for a boundary condition (Kubota et al 1998) and spectral hardening factor (Shimura & Takahara 1995) falls much below the last stable orbit for a non-spinning BH, 6Rg, where Rg = GM/c 2 is the gravitational radius. This contrasts with soft-state BHBs, where Rin generally agrees with 6Rg.…”
Section: A Comparison Of the Ulx With Bhbmentioning
confidence: 99%
“…Obviously (ii) is equivalent to (iii) and (iii) implies (iv). (v) follows from (iv) by [5] Corollary 6 and Proposition 8. Assume (v).…”
Section: Introductionmentioning
confidence: 81%
“…We shall show in a forthcoming paper [3], an extension of this fact $t\mathfrak{c}$ any open ideal of an equi-dimensional Cohen-Macaulay semi-local ring.…”
mentioning
confidence: 93%
“…Again, we may assume that $I$ is an ideal of definition and that $A/M$ are infinite fields for all maximal ideals $M$ of $A$ . Let $x_{1},$ $x_{2},$ $\cdots,$ $x_{d}$ be a system of superficial parameters of $I$ , then $e_{0}(I)=$ $\swarrow(A/(x_{1}, x_{2}, \cdots, x_{d}))$ by (3) of Lemma 4 and by the fact that $x_{d}mod$ . $(x_{1}, \cdots, x_{d-1})$ is a transversal element of $I/(x_{1}, \cdots, x_{d-1})$ .…”
mentioning
confidence: 99%
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