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

Given a valuation on the function field k(x, y), we examine the set of images of nonzero elements of the underlying polynomial ring k[x, y] under this valuation. For an arbitrary field k, a Noetherian power series is a map z : Q → k that has Noetherian (i.e., reverse well-ordered) support. Each Noetherian power series induces a natural valuation on k(x, y). Although the value groups correspondi...

This paper develops an analytical model for the multiplexing of Asynchronous Transfer Mode (ATM) connections onto the Synchronous Digital Hierarchy (SDH) Virtual Containers over an unidirectional self-healing ring. The proposed algorithm can produce a near optimal solution in pseudo-polynomial time and may be used in the ATM management entity for the real time allocation of capacity to ATM conn...

Given a valuation on the function field k(x, y), we examine the set of images of nonzero elements of the underlying polynomial ring k[x, y] under this valuation. For an arbitrary field k, a Noetherian power series is a map z : Q → k that has Noetherian (i.e., reverse well-ordered) support. Each Noetherian power series induces a natural valuation on k(x, y). Although the value groups correspondi...