An absolute ideal of an Abelian group G is a subgroup that in every ring whose additive coincides with G. We describe reduced algebraically compact groups admit at least one structure R such (Problem 93 L. Fuchs’ book “Infinite Groups”). Reduced, compact, have only fully invariant subgroups as are characterized.

Abstract Let $p$ be a prime number and $k$ an algebraically closed field with characteristic $\ell \neq p$. We show that the supercuspidal support of irreducible smooth $k$-representations Levi subgroups $\textrm {M}^{\prime}$ {SL}_n(F)$ is unique up to {M}^{\prime}$-conjugation, where $F$ either finite or non-Archimedean locally compact residual $p$.

Abstract Erdős proved that every real number is the sum of two Liouville numbers. A set W complex numbers said to have property if members . Mahler divided all transcendental into three disjoint classes S , T and U such that, in particular, any which are algebraically dependent lie same class. The a proper subset has Lebesgue measure zero. It here, using theorem Weil on locally compact groups, ...

Let d ≥ 1, and let α be an expansive Z-action by continuous automorphisms of a compact abelian group X with completely positive entropy. Then the group ∆α(X) of homoclinic points of α is countable and dense in X, and the restriction of α to the α-invariant subgroup ∆α(X) is a Z-action by automorphisms of ∆α(X). By duality, there exists a Z-action α∗ by automorphisms of the compact abelian group...

In this paper we consider Z-actions, d ≥ 1, by automorphisms of compact connected abelian groups which contain at least one expansive automorphism (such actions are called algebraic Z-actions of expansive rank one). If α is such a Z-action on an infinite compact connected abelian group X, then every expansive element α of this action has a dense group ∆αn(X) of homoclinic points. For different ...

Let X be a compact Hausdorff space and let H be a separable Hilbert space. We prove that the group of all order automorphisms of the C∗-algebra C(X)⊗ B(H) is algebraically reflexive.

In this paper we give some characterizations of topological extreme amenability. Also we answer a question raised by Ling [5]. In particular we prove that if T is a Borel subset of a locally compact semigroup S such that M(S)* has a multiplicative topological left invariant mean then T is topological left lumpy if and only if there is a multiplicative topological left invariant mean M on M(S)* ...

B. Harris [5] defined the harmonic volume for the compact Riemann surface X of genus g ≥ 3, using Chen’s iterated integrals [2]. Let J(X) be the Jacobian variety of X. By the Abel-Jacobi map X → J(X), X is embedded in J(X). By a consideration of the special harmonic volume, Harris [6] proved that the algebraic cycle F (4)−F (4) is not algebraically equivalent to zero in J(F (4)). Here, F (4) is...