Model Theory for Modules

Gennadi Puninski
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Gennadi Puninski: Moscow State Social University, Department of Mathematics

Chapter Chapter 10 in Serial Rings, 2001, pp 123-135 from Springer

Abstract: 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.

Date: 2001
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DOI: 10.1007/978-94-010-0652-1_10

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