Research reports of National institute of technology, Ube College

PISSN : 0386-4359
NCID : AN00019833

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Research reports of National institute of technology, Ube College Volume 69
published_at 2023-03

AN ALMOST DERIVED ANALOGUE OF NAKAYAMA’S LEMMA

An almost derived analogue of Nakayama's Lemma
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Abstract. As Nakayama’s lemma, in commutative ring theory, it is well-known that the residue functor of
an ideal contained in the Jacobson radical is conservative. In almost mathematics setting, considering an
almost version of perfect complexes, we prove an almost derived analogue of Nakayama’s lemma, stating
the conservativity of the derived functor of the residue of a tight ideal contained in the Jacobson radical.
Creator Keywords
Almost mathematics, derived categories.