Implications of a system of linear equations over a module

V. P. Elizarov

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) 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.

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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.