Finiteness of the number of minimal atoms in Grothendieck categories
classification
🧮 math.RT
math.CTmath.RA
keywords
minimalatomsfinitelygrothendieckmanynoetherianonlyanalogue
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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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