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Implications of a system of linear equations over a module
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V. P. Elizarov
Published/Copyright:
June 27, 2007
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.
Published Online: 2007-06-27
Published in Print: 2007-06-19
Copyright 2007, Walter de Gruyter
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Articles in the same Issue
- Quadratic assignment problems with additively monotone matrices and incomplete anti-Monge matrices: conditions for effective solvability
- Periodic properties of a simplest 2-linear shift register
- Implications of a system of linear equations over a module
- Incompatible transformations of principal ideal rings
- On a method to set up a covert channel and estimation of its tolerance for interference
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