Article
Licensed
Unlicensed
Requires Authentication
Factorially solvable rings
-
V. P. Elizarov
Published/Copyright:
February 7, 2014
Abstract
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.
Published Online: 2014-02-07
Published in Print: 2013-06
© 2014 by Walter de Gruyter GmbH & Co.
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Masthead
- Distance-regular graph with the intersection array {45, 30, 7; 1, 2, 27} does not exist
- The impact of the growth rate of the packing number of graphs on the computational complexity of the independent set problem
- Traveling salesman polytopes and cut polytopes. Affine reducibility
- Minors of the constraint matrix in multi-index transport problems
- Cycle structure of power mappings in a residue classes ring
- A criterion for the automata realizable functions to be boundedly deterministic
- On the complexity of two-dimensional discrete logarithm problem in a finite cyclic group with effective automorphism of order
- The completeness criterion for some systems containing P-sets of automaton functions
- On the synthesis of circuits admitting complete fault detection test sets of constant length under arbitrary constant faults at the outputs of the gates
- Factorially solvable rings
- Identities with permutations and quasigroups isotopic to groups and to Abelian groups
- Classes of projectively equivalent quadrics over local rings
Articles in the same Issue
- Masthead
- Distance-regular graph with the intersection array {45, 30, 7; 1, 2, 27} does not exist
- The impact of the growth rate of the packing number of graphs on the computational complexity of the independent set problem
- Traveling salesman polytopes and cut polytopes. Affine reducibility
- Minors of the constraint matrix in multi-index transport problems
- Cycle structure of power mappings in a residue classes ring
- A criterion for the automata realizable functions to be boundedly deterministic
- On the complexity of two-dimensional discrete logarithm problem in a finite cyclic group with effective automorphism of order
- The completeness criterion for some systems containing P-sets of automaton functions
- On the synthesis of circuits admitting complete fault detection test sets of constant length under arbitrary constant faults at the outputs of the gates
- Factorially solvable rings
- Identities with permutations and quasigroups isotopic to groups and to Abelian groups
- Classes of projectively equivalent quadrics over local rings
