Effective aspects of semiperfect rings

• Published in: Reports on mathematical logic Vol. 59; no. 59; pp. 3 - 26
• Main Author: Wu, Huishan
• Format: Journal Article
• Language: English
• Published: Kraków Wydawnictwo Uniwersytetu Jagiellońskiego 01.01.2024; Jagiellonian University Press; Jagiellonian University-Jagiellonian University Press
• Subjects: Linear algebra; Logic; Quotients; Rings (mathematics); Structural analysis; Theorems; local ring; Reverse mathematics; perfect rings; semiperfect rings

This paper studies effective aspects of semiperfect rings from the standpoint of reverse mathematics. Based on first-order Jacobson radicals of rings, we define a ring R with the Jacobson radical Jac(R) to be semiperfect if the quotient ring R/Jac(R) is semisimple, and idempotents of the quotient ri...