Abstract
This article studies the complexity of decomposability of rings from the perspective of computability. Based on the equivalence between the decomposition of rings and that of the identity of rings, we propose four kinds of rings, namely, weakly decomposable rings, decomposable rings, weakly block decomposable rings, and block decomposable rings. Let be the index set of computable rings. We study the complexity of subclasses of computable rings, showing that the index set of computable weakly decomposable rings is m-complete within and that the index set of computable decomposable (resp., weakly block decomposable, block decomposable) rings is m-complete within .
Citation
Huishan Wu. "The Complexity of Decomposability of Computable Rings." Notre Dame J. Formal Logic 64 (1) 1 - 14, February 2023. https://doi.org/10.1215/00294527-2023-0003
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