Direct decompositions in basic subgroups in commutative group rings. (English) Zbl 1122.16308

Summary: An attractive interplay between the direct decompositions and the explicit form of basic subgroups in group rings of Abelian groups over a commutative unitary ring is established. In particular, as a consequence, we give a simpler confirmation of a more general version of our recent result in this aspect [published in Czech. Math. J. 57, No. 1, 173-182 (2006)].


16U60 Units, groups of units (associative rings and algebras)
16S34 Group rings
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
20K21 Mixed groups
20K27 Subgroups of abelian groups
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