Factorially solvable rings

V. P. Elizarov and V. L. Kurakin


A system of linear equations over a ring R is called factorially solvable if for any proper ideal I of R its factorsystem is solvable over the ring R/I. A ring is called factorially solvable if any factorially solvable system over this ring is solvable. In this article it is shown that any decomposable ring is factorially solvable, a commutative principal ideal domain is factorially solvable if and only if it is subdirectly indecomposable, and that a finite commutative ring is factorially solvable if and only if it is not local.

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Discrete Mathematics and Applications provides the latest information on the development of discrete mathematics in Russia to a world-wide readership. The journal covers various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.