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The ℵ1-categoricity of strictly upper triangular matrix rings over algebraically closed fields

Published online by Cambridge University Press:  12 March 2014

Bruce I. Rose
Bruce I. Rose*
Affiliation:
University of Notre Dame, Notre Dame, Indiana 46556
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Abstract

Let n ≥ 3. The following theorems are proved.

Theorem. The theory of the class of strictly upper triangular n × n matrix rings over fields is finitely axiomatizable.

Theorem. If R is a strictly upper triangular n × n matrix ring over a field K, then there is a recursive map σ from sentences in the language of rings with constants for K into sentences in the language of rings with constants for R such that K ⊨ φ if and only if R φ σ(φ).

Theorem. The theory of a strictly upper triangular n × n matrix ring over an algebraically closed field is ℵ1-categorical.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 43 , Issue 2 , June 1978 , pp. 250 - 259
Copyright
Copyright © Association for Symbolic Logic 1978

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References

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