We study transcendency properties for graded field extension and give an application to valued field extensions. 1. Introduction. An important tool to study rings with valuation is the so-called associated graded ring construction: to a valuation ring R, we can associate a ring gr(R) graded by the valuation group. This ring is often easier to study, and one tries to lift properties back from gr...

Dibromination of [2.2]paracyclophane (I) led to predominantly pseudo-ortho2 (11) and pseudo-para2 (111) disubstituted compounds, and to lesser amounts of pseudo-meta (IV) and para (V) isomers. Oxidation of these dibromides gave terephthalic acids whose esters were identified by vpc, and whose structures allowed homoannular and transannular bromination to be differentiated. Tetrabromination of I...

In the title compound, C20H16N2O2, the condensed tricyclic fragment is near to planar, with an r.m.s. deviation of 0.0531 Å. The 1,4-di-hydro-pyridine (1,4-DHP) ring adopts a slightly puckered boat-like conformation. The N and opposite C atoms deviate from the least-squares plane of the four other ring atoms by 0.039 (3) and 0.141 (3) Å, respectively. The C=O group located at the tricyclic frag...

We characterize the polynomial closure of a pseudo-convergent sequence in valuation domain V arbitrary rank, and then we use this result to show that is never topological when has rank at least 2.

Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P^{&minus1} is a ring. In fact, it is proved that P^{&minus1} = (P : P) if and only if P is not invertible. Furthermore, if P is invertib...

in this paper, we introduce the notion of ($epsilon $, $epsilon $ $vee$ q_{k})− fuzzy subnear-ring which is a generalization of ($epsilon $, $epsilon $ $vee$ q)−fuzzy subnear-ring. we have given examples which are ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy ideals but they are not ($epsilon $, $epsilon $ $vee$ q)−fuzzy ideals. we have also introduced the notions of ($epsilon $, $epsilon $ $vee$ ...

We present a deep near-infrared wide-angle photometric analysis of the structure of the inner Galactic bar and central disk. The presence of a triaxial structure at the centre of the Galaxy is confirmed, consistent with a bar inclined at 22±5.5 • from the Sun-Galactic centre line, extending to about 2.5 kpc from the Galactic centre and with a rather small axis ratio. A feature at ℓ=−9.8 • not a...

1.1. The p-adic measure. Let p be a prime number. We consider a field K with a valuation ord : K× → Z, extended to K by ord(0) = ∞. We denote by OK the valuation ring OK = {x ∈ K|ord(x) ≥ 0} and we fix an uniformizing parameter $, that is, an element of valuation 1 in OK . The ring OK is a local ring with maximal ideal MK of OK generated by $. We shall assume the residue field k := OK/MK is fin...