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- Title
Ring structure theorems and arithmetic comprehension.
- Authors
Wu, Huishan
- Abstract
Schur's Lemma says that the endomorphism ring of a simple left R-module is a division ring. It plays a fundamental role to prove classical ring structure theorems like the Jacobson Density Theorem and the Wedderburn–Artin Theorem. We first define the endomorphism ring of simple left R-modules by their Π 1 0 subsets and show that Schur's Lemma is provable in R C A 0 . A ring R is left primitive if there is a faithful simple left R-module and left semisimple if the left regular module R R is semisimple. The Jacobson Density Theorem and the Wedderburn-Artin Theorem characterize left primitive ring and left semisimple ring, respectively. We then study such theorems from the standpoint of reverse mathematics.
- Subjects
REVERSE mathematics; DIVISION rings; ARITHMETIC; COMPREHENSION; ENDOMORPHISM rings
- Publication
Archive for Mathematical Logic, 2021, Vol 60, Issue 1/2, p145
- ISSN
0933-5846
- Publication type
Article
- DOI
10.1007/s00153-020-00738-3