We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Reverse mathematics and semisimple rings.
- Authors
Wu, Huishan
- Abstract
This paper studies various equivalent characterizations of left semisimple rings from the standpoint of reverse mathematics. We first show that A C A 0 is equivalent to the statement that any left module over a left semisimple ring is semisimple over R C A 0 . We then study characterizations of left semisimple rings in terms of projective modules as well as injective modules, and obtain the following results: (1) A C A 0 is equivalent to the statement that any left module over a left semisimple ring is projective over R C A 0 ; (2) A C A 0 is equivalent to the statement that any left module over a left semisimple ring is injective over R C A 0 ; (3) R C A 0 proves the statement that if every cyclic left R-module is projective, then R is a left semisimple ring; (4) A C A 0 proves the statement that if every cyclic left R-module is injective, then R is a left semisimple ring.
- Subjects
REVERSE mathematics; GORENSTEIN rings
- Publication
Archive for Mathematical Logic, 2022, Vol 61, Issue 5/6, p769
- ISSN
0933-5846
- Publication type
Article
- DOI
10.1007/s00153-021-00812-4