Abstract
With every ring R one can connect the first order language L R (see [29]), which symbols are the equality, the constant 0 and the functional symbols: the binary ‘+’ and, for every r ∈ R, the unary function which will be denoted by the same letter. The axioms of this theory can be written in a natural way (see [29]) such that its models are exactly the right unitary modules over R. For instance, for every r, s ∈ R there are the following axioms: ∀x x(r + s) = xr + xs and ∀x x(rs) = (xr)s.
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© 2001 Springer Science+Business Media Dordrecht
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Puninski, G. (2001). Model Theory for Modules. In: Serial Rings. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0652-1_10
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DOI: https://doi.org/10.1007/978-94-010-0652-1_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3862-1
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