We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to S nor to S. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms fr...

In this paper we study the second Hochschild cohomology group HH(Λ) of a finite dimensional algebra Λ. In particular, we determine HH(Λ) where Λ is a finite dimensional self-injective algebra of finite representation type over an algebraically closed field K and show that this group is zero for most such Λ; we give a basis for HH(Λ) in the few cases where it is not zero.

Let τ be a hereditary torsion theory on the category R-Mod of left R-modules over an associative unitary ring R. We introduce the notion of τ-natural class as a class of modules closed under τ-dense submodules, direct sums, and τ-injective hulls. We study connections between certain conditions involving τ-(quasi-)injectivity in the context of τnatural classes, generalizing results established b...

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...

Let A and B be C*-algebras $$\varphi :A\rightarrow B$$ a $$*$$ -homomorphism. We discuss the properties of kernel (co-)image induced map $$\mathrm {K}_{0}(\varphi ):\mathrm {K}_{0}(A) \rightarrow \mathrm {K}_{0}(B)$$ on level K-theory. In particular, we are interested in case that co-image is torsion free, show it holds when commutative unital, has real rank zero, $$ unital injective. also embe...

Abstract We study distinguished objects in the category $\mathcal{B}\mathcal{L}$ of Banach lattices and lattice homomorphisms. The free construction introduced by de Pagter Wickstead [ 8] generates push-outs, combining this with an old result Kellerer 17] on marginal measures, amalgamation property is established. This will be key tool to prove that $L_1([0,1]^{\mathfrak{c}})$ separably $\mathc...

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 $R\propto R$

An easy consequence of this is that a left Noetherian (respectively left Artinian) ring which is finitely generated over its center is right Noetherian (respectively right Artinian). Theorem 1 follows easily from Theorem 2, which gives a partial converse to the following standard fact: IfR C S are rings, and ifQ is an injective R-module, then Hom~(S, Q) is an injective S-module (this follows, f...

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...