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...

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...

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...

Let V (resp. D) be a valuation domain (resp. SFT Prüfer domain), I a proper ideal, and V̂ (resp. D̂) be the I-adic completion of V (resp. D). We show that (1) V̂ is a valuation domain, (2) Krull dimension of V̂ = dimV I+1 if I is not idempotent, V̂ ∼= V I if I is idempotent, (3) dim D̂ = dimD I + 1, (4) D̂ is an SFT Prüfer ring, and (5) D̂ is a catenarian ring. Throughout this paper, all rings are assu...

The six-membered thio-pyran ring in the title compound, C(24)H(19)BrS, adopts an approximate envelope conformation, with the S atom displaced by 0.26 (1) Å and the 2-methyl-ene C atom by -0.54 (1) Å from the plane of the other four sp(2)-hydridized C atoms. The methyl substituent on the methyl-ene carbon lies in a pseudo-axial position with the phenyl ring in a pseudo-equatorial position.

The six-membered thio-pyran ring in the title compound, C(26)H(24)S, adopts a boat conformation, with the S atom displaced by 0.478 (2) Å and the 3-methyl-ene C atom by 0.644 (2) Å from the plane of the other four sp(2)-hydridized C atoms. The methyl group on the methyl-ene carbon lies in a pseudo-equatorial position and the phenyl ring in a pseudo-axial position.

Let V be a valuation domain of rank one with quotient field K. We study the set extensions to rational functions K(X) induced by pseudo-convergent sequences K from topological point view, endowing this either Zariski or constructible topology. In particular, we consider two subspaces prescribed breadth pseudo-limit. give some necessary conditions for space metrizable (under topology) in terms v...

We partially generalize the known results on dp-minimal fields to dp-finite fields. prove a dichotomy: if K is sufficiently saturated expansion of field, then either has finite Morley rank or non-trivial Aut(K/A)-invariant valuation ring for some small set A. In positive characteristic case, we can even obtain henselian ring. Using this, classify pure