Generalised reduced modules

Kyomuhangi, Annet; Ssevviiri, David

doi:10.1007/s12215-021-00686-8

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David Ssevviiri1

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2024

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“…Therefore, it is amenable to study by use of category theory. The use of this method to study reduced modules first appeared in [12] and [13]. In this paper, we continue with this approach; it allows us to benefit from the powerful machinery of category theory.…”

Section: David Ssevviirimentioning

confidence: 99%

Applications of reduced and coreduced modules I

Ssevviiri¹

2024

International Electronic Journal of Algebra

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This is the first in a series of papers highlighting the applications of reduced and coreduced modules. Let $R$ be a commutative unital ring and $I$ be an ideal of $R$. We show that $I$-reduced $R$-modules and $I$-coreduced $R$-modules provide a setting in which the Matlis-Greenless-May (MGM) Equivalence and the Greenless-May (GM) Duality hold. These two notions have been hitherto only known to exist in the derived category setting. We realise the $I$-torsion and the $I$-adic completion functors as representable functors and under suitable conditions compute natural transformations between them and other functors.

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Section: David Ssevviirimentioning

confidence: 99%