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Remarks on balance in generalized Tate cohomology
Authors:Alina Iacob
Affiliation:(1) Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027, USA
Abstract:We consider two pairs of complete hereditary cotorsion theories $${left( {mathcal{P},mathcal{M}} right)},{left( {mathcal{M},mathcal{I}} right)};{text{and}};{left( {mathcal{C},mathcal{L}} right)}{left( {mathcal{L},mathcal{E}} right)}$$ on the category of left R-modules, such that $$mathcal{P} subset mathcal{C}.$$ We prove that for any left R-modules M, N and for any n ≧ 1, the generalized Tate cohomology modules $$widehat{{{text{Ext}}}}^{n}_{{mathcal{C},mathcal{P}}} {left( {M,N} right)}$$ can be computed either using a left $$mathcal{C}{text{ - resolution}}$$ of M and a left $$mathcal{P}{text{ - resolution}}$$ of M or using a right $$mathcal{E}hbox{-and}$$ a right $$mathcal{I}{text{ - resolution}}$$ of N. Received: 17 December 2004
Keywords:18G25  16E30
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