论文信息 - On the model theory of the ring NT(n, R)

On the model theory of the ring NT(n, R)

Abstract Let NT(n, R) be the ring of strictly upper triangular(n × n) matrices (n ≥ 3) over an associative ring R with 1. We study the rings elementarily equivalent to NT(n, R) and find their structure. We prove the following theorems: • Theorem 1. NT(n, S) is elementarily equivalent to NT(m, R) if and only if n = m and R is equivalent to S. • Theorem 2. The number of models size λ elementarily equivalent to NT(n, R) equals the number of rings of size λ elementarily equivalent to R.

Carlos R. Videla

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