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  1. Structure of semisimple rings in reverse and computable mathematics.Huishan Wu - 2023 - Archive for Mathematical Logic 62 (7):1083-1100.
    This paper studies the structure of semisimple rings using techniques of reverse mathematics, where a ring is left semisimple if the left regular module is a finite direct sum of simple submodules. The structure theorem of left semisimple rings, also called Wedderburn-Artin Theorem, is a famous theorem in noncommutative algebra, says that a ring is left semisimple if and only if it is isomorphic to a finite direct product of matrix rings over division rings. We provide a proof for the (...)
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  • Two kinds of fixed point theorems and reverse mathematics.Weiguang Peng & Takeshi Yamazaki - 2017 - Mathematical Logic Quarterly 63 (5):454-461.
    In this paper, we investigate the logical strength of two types of fixed point theorems in the context of reverse mathematics. One is concerned with extensions of the Banach contraction principle. Among theorems in this type, we mainly show that the Caristi fixed point theorem is equivalent to math formula over math formula. The other is dedicated to topological fixed point theorems such as the Brouwer fixed point theorem. We introduce some variants of the Fan-Browder fixed point theorem and the (...)
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