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n -flat and n -FP-injective modules

Xiao Yan Yang, Zhongkui Liu (2011)

Czechoslovak Mathematical Journal

In this paper, we study the existence of the n -flat preenvelope and the n -FP-injective cover. We also characterize n -coherent rings in terms of the n -FP-injective and n -flat modules.

Newton and Schinzel sequences in quadratic fields

David Adam, Paul-Jean Cahen (2010)

Actes des rencontres du CIRM

We give the maximal length of a Newton or a Schinzel sequence in a quadratic extension of a global field. In the case of a number field, the maximal length of a Schinzel sequence is 1, except in seven particular cases, and the Newton sequences are also finite, except for at most finitely many cases, all real. We give the maximal length of these sequences in the special cases. We have similar results in the case of a quadratic extension of a function field 𝔽 q ( T ) , taking in account that the ring of integers...

Noetherian loop spaces

Natàlia Castellana, Juan Crespo, Jérôme Scherer (2011)

Journal of the European Mathematical Society

The class of loop spaces of which the mod p cohomology is Noetherian is much larger than the class of p -compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as P and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space B X of such an object and prove it is as small as expected, that is, comparable to that of B P . We also show that B X differs basically from the classifying space of a p -compact group...

Non-axiomatizability of real spectra in λ

Timothy Mellor, Marcus Tressl (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

We show that the property of a spectral space, to be a spectral subspace of the real spectrum of a commutative ring, is not expressible in the infinitary first order language λ of its defining lattice. This generalises a result of Delzell and Madden which says that not every completely normal spectral space is a real spectrum.

Noncommutative del Pezzo surfaces and Calabi-Yau algebras

Pavel Etingof, Victor Ginzburg (2010)

Journal of the European Mathematical Society

The hypersurface in 3 with an isolated quasi-homogeneous elliptic singularity of type E ˜ r , r = 6 , 7 , 8 , has a natural Poisson structure. We show that the family of del Pezzo surfaces of the corresponding type E r provides a semiuniversal Poisson deformation of that Poisson structure. We also construct a deformation-quantization of the coordinate ring of such a del Pezzo surface. To this end, we first deform the polynomial algebra [ x 1 , x 2 , x 3 ] to a noncommutative algebra with generators x 1 , x 2 , x 3 and the following 3 relations labelled...

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