Publication at Faculty of Mathematics and Physics |
2012
Abstract
By applying classical results of combinatorial set theory we prove necessary conditions satisfied by dimension sequences of abelian regular semiartinian rings. On the other hand, we present constructions of commutative regular semiartinian rings with given ranks of slices of socle chain.
In some particular cases we prove a necessary and sufficient condition under which there exists an abelian regular semiartinian ring with given ranks of slices.