Complete exact sequences
Completely decomposable abelian groups any pure subgroup of which is completely decomposable
Completely decomposable abelian groups any regular subgroup of which is completely decomposable
Completely decomposable pure subgroups of completely decomposable abelian groups
Completing codes
Complex Hadamard matrices and the spectral set conjecture.
By analyzing the connection between complex Hadamard matrices and spectral sets, we prove the direction "spectral ⇒ tile" of the Spectral Set Conjecture, for all sets A of size |A| ≤ 5, in any finite Abelian group. This result is then extended to the infinite grid Zd for any dimension d, and finally to Rd.
Computation of the mapping of factorization by the radical for of the endomorphism ring.
Concerning Abelian-Regular Transitive Triple Systems
Concerning almost divisible torsion free abelian groups
Conservation Rules of Direct Sum Decomposition of Groups
In this article, conservation rules of the direct sum decomposition of groups are mainly discussed. In the first section, we prepare miscellaneous definitions and theorems for further formalization in Mizar [5]. In the next three sections, we formalized the fact that the property of direct sum decomposition is preserved against the substitutions of the subscript set, flattening of direct sum, and layering of direct sum, respectively. We referred to [14], [13] [6] and [11] in the formalization.
Constructing subsets of a given packing index in Abelian groups
Construction of group topologies on abelian groups
Correction to "On classes of abelian groups" (Fundamenta Mathematicae 51(1962), pp. 149-178)
Corrigendum to "An improvement on Olson's constant for ℤₚ ⊕ ℤₚ" (Acta Arith. 141 (2010), 311-319)
Cotorsion-free algebras as endomorphism algebras in - the discrete and topological cases
The discrete algebras over a commutative ring which can be realized as the full endomorphism algebra of a torsion-free -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, . Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological...
Countable extensions of torsion Abelian groups
Suppose is an abelian torsion group with a subgroup such that is countable that is, in other words, is a torsion countable abelian extension of . A problem of some group-theoretic interest is that of whether , a class of abelian groups, does imply that . The aim of the present paper is to settle the question for certain kinds of groups, thus extending a classical result due to Wallace (J. Algebra, 1981) proved when coincides with the class of all totally projective -groups.
Covering abelian groups with cyclic subsets.
Cube tilings as contributions of algebra to geometry.