In this paper, it is shown that the Boolean ring of a commutative isomorphic to clopens its prime spectrum. particular, Stone's Representation Theorem generalized. The spectrum given R identified with Pierce R. discreteness spectra characterized. It also proved space connected components compact X X. As another major result, morphism rings between complete preserves suprema if and only induced ...

We described in [M1] a monoid b G, the face monoid, acting on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid whose unit group is a Kac-Moody group G. We found in [M5] two natural extensions of the action of the Kac-Moody group G on its building Ω to actions of the face monoid b G on the building Ω....

Semiclassical limits of generic multiparameter quantized coordinate rings A = Oq(k ) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric matrix whose entries generate a torsionfree subgroup of k. A semiclassical limit of A is a Poisson algebra structure on the corresponding classical coordinate ring...

In this paper S will denote an AG-groupoid. A two-sided ideal I of S is called a right (left) pure ideal of S , if for each x in I , there is an element y in I such that ) = ( = x yx x xy . A left (right) pure ideal I is called purely prime if it is proper and if for any pure ideals 1 I and 2 I : I I I 2 1 implies I I1 or I I2 . Analogous to the construction of the pure spectrum of a semigroup ...

This paper concerns contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a common characteristic of these functors: every such functor assigns the empty set to Mn(C) for n ≥ 3. The proof relies, in part, on the Kochen-Specker Theorem of qu...

In this paper, we study the cobordism spectrum MO〈8〉 at the prime 3. This spectrum is important because it is conjectured to play the role for elliptic cohomology that Spin cobordism plays for real K-theory. We show that the torsion is all killed by 3, and that the Adams-Novikov spectral sequence collapses after only 2 differentials. Many of our methods apply more generally.

This paper shows the existence of a class of block transitive meager squares of order q on GF (q) for odd prime q, q large. Using these meager squares along with other known meager system constructions, we determine the spectrum of orders that admit meager systems: all odd n, n ≥ 9. Using this result, it is also determined that the spectrum of orders that admit 5-sparse Steiner triple systems i...

We employ an infinite-signature Hrushovski amalgamation construction to yield two results in Recursive Model Theory. The first result, that there exists a strongly minimal theory whose only recursively presentable models are the prime and saturated models, adds a new spectrum to the list of known possible spectra. The second result, that there exists a strongly minimal theory in a finite langua...

Abstract LaO bands are a characteristic feature in the spectrum of cool S-type stars. La is made primarily by s -process during asymptotic giant branch phase stellar evolution. The B 2 Σ + –X and A Π–X band systems can be used to determine abundances S with v <mml:mo accent="fals...

In this paper, we study the cobordism spectrum MOh8i at the prime 3. This spectrum is important because it is conjectured to play the role for elliptic cohomology that Spin cobordism plays for real K-theory. We show that the torsion is all killed by 3, and that the Adams-Novikov spectral sequence collapses after only 2 diierentials. Many of our methods apply more generally.