Arbitrary models of the complete first-order theories of FDZ-rings
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908919549394944 |
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| author | Sohrabi, Mahmood |
| author_facet | Sohrabi, Mahmood |
| contents | In this paper, we study arbitrary models of the first-order theory of a ring $A$ where the additive group $A$ is a finitely generated abelian group. Following an earlier paper by this author, Alexei G. Myasnikov and Francis Oger, we call these rings the FDZ-rings or FDZ-algebras. The rings considered are not necessarily unitary, commutative, or associative. We provide criteria for such rings to be quasi finitely axiomatizable (QFA) or bi-interpretable with the ring of integers $\mathbb Z$. We shall also describe all rings elementarily equivalent to such a ring $A$ given certain constraints on $A$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_27730 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Arbitrary models of the complete first-order theories of FDZ-rings Sohrabi, Mahmood Logic Rings and Algebras 03, 13, 17 In this paper, we study arbitrary models of the first-order theory of a ring $A$ where the additive group $A$ is a finitely generated abelian group. Following an earlier paper by this author, Alexei G. Myasnikov and Francis Oger, we call these rings the FDZ-rings or FDZ-algebras. The rings considered are not necessarily unitary, commutative, or associative. We provide criteria for such rings to be quasi finitely axiomatizable (QFA) or bi-interpretable with the ring of integers $\mathbb Z$. We shall also describe all rings elementarily equivalent to such a ring $A$ given certain constraints on $A$. |
| title | Arbitrary models of the complete first-order theories of FDZ-rings |
| topic | Logic Rings and Algebras 03, 13, 17 |
| url | https://arxiv.org/abs/2603.27730 |