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This paper investigates the productivity of the Zariski topology $ℨ_{G}$ of a group $G$ . If $𝒢 = {G_{i} ∣ i \in I}$ is a family of groups, and $G = \prod_{i \in I} G_{i}$ is their direct product, we prove that $ℨ_{G} \subseteq \prod_{i \in I} ℨ_{G_{i}}$ . This inclusion can be proper in general, and we describe the doubletons $𝒢 = {G_{1}, G_{2}}$ of abelian groups, for which the converse inclusion holds as well, i.e., $ℨ_{G} = ℨ_{G_{1}} \times ℨ_{G_{2}}$ . If $e_{2} \in G_{2}$ is the identity element of a group $G_{2}$ , we also describe the class $Δ$ of groups $G_{2}$ such that $G_{1} \times {e_{2}}$ is an elementary algebraic subset of $G_{1} \times G_{2}$ for every group $G_{1}$ . We show among others, that $Δ$ is stable...

Pure extensions of locally compact abelian groups

Peter Loth (2006)

Rendiconti del Seminario Matematico della Università di Padova

Pure subgroups split

Ladislav Bican (1979)

Commentationes Mathematicae Universitatis Carolinae

Quasi-balanced torsion-free groups

H. Pat Goeters, William Ullery (1998)

Commentationes Mathematicae Universitatis Carolinae

An exact sequence $0 \to A \to B \to C \to 0$ of torsion-free abelian groups is quasi-balanced if the induced sequence $0 \to 𝐐 \otimes Hom (X, A) \to 𝐐 \otimes Hom (X, B) \to 𝐐 \otimes Hom (X, C) \to 0$ is exact for all rank-1 torsion-free abelian groups $X$ . This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which $C$ is a Butler group. The special case where $B$ is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced...

Quasi-Direct Decompositions of Torsion-Free Abelian Groups of Infinite Rank.

L. Fuchs, G. Viljoen (1973)

Mathematica Scandinavica

Quasi-isomorphism and $ℤ_{(2)}$ -representations for a class of Butler groups

H. Pat Goeters, Charles Megibben (2001)

Rendiconti del Seminario Matematico della Università di Padova

Quasiprojective and quasi-injective finite valuated groups

C. Vinsonhaler, W. Wickless (1981)

Colloquium Mathematicae

Quotients of reflexive modules

Manfred Dugas, Rüdiger Göbel (1981)

Fundamenta Mathematicae

Regular submodules of torsion modules over a discrete valuation domain

Pudji Astuti, Harald K. Wimmer (2006)

Czechoslovak Mathematical Journal

A submodule $W$ of a $p$ -primary module $M$ of bounded order is known to be regular if $W$ and $M$ have simultaneous bases. In this paper we derive necessary and sufficient conditions for regularity of a submodule.

Regularität in torsionsfreien abelschen Gruppen

Edgar Müller, Otto Mutzbauer (1992)

Czechoslovak Mathematical Journal

Rings on certain classes of torsion-free Abelian groups

Barry J. Gardner, David R. Jackett (1976)

Commentationes Mathematicae Universitatis Carolinae

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