We show that closed aspherical manifolds supporting an affine structure, whose holonomy map is injective and contains a pure translation, must have vanishing simplicial volume. This provides some further evidence for the veracity of the Auslander Conjecture. Along the way, we provide a simple cohomological criterion for aspherical manifolds with normal amenable subgroups of π1 to have vanishing...

A ring $R$ is called right CSP if the sum of any two closed ideals also a ideal $R$. Left rings can be defined similarly. An example given to show that left may not CSP. It shown matrix over proved $\mathbb{M}_{2}(R)$ and only self-injective von Neumann regular. The equivalent characterization for trivial extension $R\propto R$

Carrying further work of T.A. Crawford, we show that each component of the space of harmonic maps from the 2-sphere to complex projective 2-space of degree d and energy 4πE is a smooth closed submanifold of the space of all C j maps (j ≥ 2). We achieve this by showing that the Gauss transform which relates them to spaces of holomorphic maps of given degree and ramification index is smooth and h...

Abstract We generalize Bloch’s map on torsion cycles from algebraically closed fields to arbitrary fields. While over is injective for zero-cycles and of codimension at most two, we show that the generalization only two but, in general, not zero-cycles. Our result implies Jannsen’s cycle class integral $\ell $ -adic continuous étale cohomology is, finitely generated This answers a question Scav...

Abstract We consider the smallest triangulated subcategory of unbounded derived module category a ring that contains injective modules and is closed under set indexed coproducts. If this entire category, then we say injectives generate for ring. In particular, ask whether, if collection rings, do related constructions, vice versa. provide sufficient conditions statement to hold various construc...

In this paper we introduce a generalization of M-small modules and discuss about the torsion theory cogenerated by this kind of modules in category . We will use the structure of the radical of a module in  and get some suitable results about this class of modules. Also the relation between injective hull in  and this kind of modules will be investigated in this article.   For a module  we show...

1. We announce here the following result: Two homotopic diffeomorphisms of a paracompact separable Hubert manifold of infinite dimension are isotopic. (1) In this paper, a hilbert manifold (A-manifold) with or without boundary is always hausdorff, paracompact, separable C°°-differentiable and with the infinite dimensional separable hilbert space H as local model. Let M(M, dM) be an /^-manifold ...

Let U be the set of prime ideals P completion a Stanley–Reisner ring S, such that localization at Frobenius algebra injective hull residue field S is finitely generated algebra. We give partial answer to conjecture made by M. Katzman about openness U. Specifically, we show has non-empty interior and present some sufficient conditions for principal open D(f) contained in U, intersections closed ...

It is proved that EJ is injective if E is an injective module over a valuation ring R, for each prime ideal J 6= Z. Moreover, if E or Z is flat, then EZ is injective too. It follows that localizations of injective modules over h-local Prüfer domains are injective too. If S is a multiplicative subset of a noetherian ring R, it is well known that SE is injective for each injective R-module E. The...

We obtain some results about Borel maps with meager fibers on completely metrizable separable spaces. The results are related to a recent dichotomy by Sabok and Zapletal, concerning Borel maps and σ-ideals generated by closed sets. In particular, we give a “classical” proof of this dichotomy. We shall also show that for certain natural σ-ideals I generated by closed sets in compact metrizable s...