Applications of reduced and coreduced modules I

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International Electronic Journal of Algebra
Volume:35 Issue:35
Applications of reduced and coreduced modules I

Applications of reduced and coreduced modules I

Pages : 61-81

View : 123 | Download : 194

Publication Date : 2024-01-09

Article Type : Research Paper

Abstract :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.
Keywords : torsion and adic completion, coreduced module, reduced module

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