This paper offers an expository account of some ideas, methods, and conjectures concerning quantized coordinate rings and their semiclassical limits, with a particular focus on primitive ideal spaces. The semiclassical limit of a family of quantized coordinate rings of an affine algebraic variety V consists of the classical coordinate ring O(V ) equipped with an associated Poisson structure. Co...

In the title mol-ecule, [V(C(15)H(10)I(2)N(2)O(2))(CH(3)O)O(CH(3)OH)], the V(V) atom is coordinated by one N and two O atoms from an N'-(3,5-diiodo-2-oxidobenzyl-idene-κO)-4-methyl-benzo-hydra-zidate (L) ligand, one oxide O atom, one methano-late [V-O = 1.761 (3) Å] and one methanol [V-O = 2.383 (4) Å] O atom in a distorted octa-hedral geometry. In the L ligand, the two benzene rings are nearly...

For an o-minimal expansion R of a real closed field and a set V of Th(R)-convex valuation rings, we construct a “pseudo completion” with respect to V . This is an elementary extension S of R generated by all completions of all the residue fields of the V ∈ V , when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings u...

Transformation of self-assembled InAs quantum dots (QDs) on InP(100) into quantum rings (QRs) is studied. In contrast to the typical approach to III--V semiconductor QR growth, the QDs are not capped to form rings. Atomic force micrographs reveal a drastic change from InAs QDs into rings after a growth interruption in tertiarybutylphosphine ambient. Strain energy relief in the InAs QD is discus...

let $r$ be an associative ring with identity and $z^*(r)$ be its set of non-zero zero divisors.  the zero-divisor graph of $r$, denoted by $gamma(r)$, is the graph whose vertices are the non-zero  zero-divisors of  $r$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  in this paper, we bring some results about undirected zero-divisor graph of a monoid ring ov...

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ = ( T M D 0 U N 0 0 V )