Homological Dimensions in Cotorsion Pairs

2008/08/11 by Hugel, Lidia Angeleri, Hernandez, Octavio Mendoza
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0808.1585

Abstract

Two classes \mathcal A and \mathcal B of modules over a ring R are said to form a cotorsion pair (\mathcal A, \mathcal B) if \mathcal A=\rm Ker Ext¹_R(-,\mathcal B) and \mathcal B=\rm Ker Ext¹_R(\mathcal A,-). We investigate relative homological dimensions in cotorsion pairs. This can be applied to study the big and the little finitistic dimension of R. We show that \Findim R

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