V. P. Elizarov
Implications of a system of linear equations over a module
We describe the class L(R) of all left modules over a ring R such that for any matrix D over R and any solvable system of equations Fη? = γ? over a module from L(R) the system of
equations Aξ? = β? is its D-implication if and only if T(F, γ?) = (AD,β?) for some matrix T .
If R is a quasi-Frobenius ring, then L(R) contains the subclass of all faithful R-modules. A criterion for a system of equations over a module from L(R) to be definite is obtained.
Discrete Mathematics and Applications, Walter de Gruyter
Print ISSN: 0924-9266
Volume: 17, 06/2007
Pages: 163 - 169
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