Jeff Smith's Theory of Ideals
Robert R. Bruner, Daniel C. Isaksen

TL;DR
This paper examines Jeff Smith's 2006 theory of ideals within triangulated symmetric monoidal categories, demonstrating its equivalence to a specific bimodule map, thereby clarifying its algebraic structure.
Contribution
It establishes the equivalence between Smith's ideal definition and a central bimodule map, providing a clearer algebraic understanding of the theory.
Findings
Smith's ideals are equivalent to central bimodule maps
The paper clarifies the algebraic structure of ideals in ring spectra
Provides a foundation for further algebraic exploration in monoidal categories
Abstract
In 2006, Jeff Smith proposed a theory of ideals for rings in a triangulated symmetric monoidal category such as ring spectra or DGAs. We show that his definition is equivalent to a `central' --bimodule map .
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras · Commutative Algebra and Its Applications
