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Model Theory for Modules

In: Serial Rings

Author

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  • Gennadi Puninski

    (Moscow State Social University, Department of Mathematics)

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.

Suggested Citation

  • Gennadi Puninski, 2001. "Model Theory for Modules," Springer Books, in: Serial Rings, chapter 0, pages 123-135, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-0652-1_10
    DOI: 10.1007/978-94-010-0652-1_10
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