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arXiv · 1503.02116

Finiteness of the number of minimal atoms in Grothendieck categories

Ryo Kanda
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Abstract

For a Grothendieck category having a noetherian generator, we prove that there are only finitely many minimal atoms. This is a noncommutative analogue of the fact that every noetherian scheme has only finitely many irreducible components. It is also shown that each minimal atom is represented by a compressible object.

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BibTeXRIS

Ryo Kanda. 2015-03-07. Finiteness of the number of minimal atoms in Grothendieck categories. https://doi.org/10.1016/j.jalgebra.2019.03.003

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