An Ohm–Rush algebra $$R \rightarrow S$$ is called McCoy if for any zero-divisor f in S, its content c(f) has nonzero annihilator R, because proved this when $$S=R[x]$$ . We answer a question of Nasehpour by giving class examples faithfully flat algebras with the property that are not weak algebras. However, we show iff $$R/I S/I all radical (resp. prime) ideals I R. When R Noetherian (or more g...

After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois extensions) can be given geometric meaning extending their geometric interpretations in the commutative case. On the other hand, we show that some constructions...

This article is made up with two parts. In the first part, using a recent result of Schauenburg, one generalizes to the case when objects are faithfully flat over the ground ring, the full equivalence between the notions of Hopf-Galois objects and Hopf-Galois systems. In this last description, one gives explicitly an inverse for a Hopf-Galois object T together with its generalized antipode. In ...

After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois extensions) can be given geometric meaning extending their geometric interpretations in the commutative case. On the other hand, we show that some constructions...

Let H be a finite-dimensional Hopf algebra. We study the behaviour of primitive and maximal ideals in certain types of ring extensions determined by H . The main focus is on the class of faithfully flat Galois extensions, which includes includes smash and crossed products. It is shown how analogous results can be obtained for the larger class of extensions possessing a total integral, which inc...

The cathode ray is practically free from inertia and therefore an ideal instrumentality for studying variations in electrical potential. A cathode ray oscilloscope with an amplifier system of high frequency response and an expanded time scale, 330 mm. per second, were employed to record electrocardiograms. Such tracings revealed considerable notching, slurring, and other peculiarities not seen ...

Let H be a commutative faithfully flat Hopf algebra over a commutative ring R. We give an exact sequence describing the group of H-Galois coobjects. The other terms in the sequence are Harrison cohomology groups. This generalizes an exact sequence due to Early and Kreimer and Yokogawa. Résumé Soit H une algèbre de Hopf commutative fidèlement plate sur un anneau commutatif R. Nous étudions une s...

We associate to every equicharacteristic zero Noetherian local ring R a faithfully flat ring extension which is an ultraproduct of rings of various prime characteristics, in a weakly functorial way. Since such ultraproducts carry naturally a non-standard Frobenius, we can define a new tight closure operation on R by mimicking the positive characteristic functional definition of tight closure. T...

Abstract Some false vacua do not decay via bounces. This usually happens when a flat direction of the tunneling action due to scale invariance is lifted sloping valley by breaking perturbation, pushing bounce off infinity. We compare two types alternative configurations that have been proposed recently describe in such cases: pseudo-bounces and new instantons. Although both field are quite simi...