Submission date: 24 January 2023

Abstract:

Here we work in an arbitrary (but fixed) o-minimal expansion of a dense linearly ordered set. We say that a definable ring is definably semiprime if squares of nontrivial two-sided ideals definable in the expansion are non-trivial. We prove a definable version of Wedderburn-Artin Theorem and give a characterization of definably semiprime rings.

Mathematics Subject Classification: Primary 03C64; Secondary 16D25, 16D60, 16K20

Keywords and phrases: o-minimality, definable ring, definably semiprime, Wedderburn-Artin Theorem

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