Absolute Ideals of Algebraically Compact Abelian Groups
نویسندگان
چکیده
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.
منابع مشابه
On component extensions locally compact abelian groups
Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...
متن کاملBracket Products on Locally Compact Abelian Groups
We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).
متن کاملLocally compact abelian groups
These notes are a gloss on the first chapter of Walter Rudin’s Fourier Analysis on Groups, and may be helpful to someone reading Rudin. The results I do prove are proved in more detail than they are in Rudin. I caution that before reading the first chapter of that book it is know about the Gelfand transform on commutative Banach algebras because results from that are used without even stating t...
متن کاملDefinably compact abelian groups
Let M be an o–minimal expansion of a real closed field. Let G be a definably compact definably connected abelian n–dimensional group definable in M. We show the following: the o–minimal fundamental group of G is isomorphic to Z; for each k > 0, the k–torsion subgroup of G is isomorphic to (Z/kZ), and the o–minimal cohomology algebra over Q of G is isomorphic to the exterior algebra over Q with ...
متن کاملPseudoframe multiresolution structure on abelian locally compact groups
Let $G$ be a locally compact abelian group. The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$. Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level. Also, the construction of affine frames for $L^2(G)$ bas...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2021
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-021-05634-6