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We derive in the paper the tensor product functor $-\otimes_R-$ by using proper $\mathcal {G}\mathcal {P}_C$-resolutions, where $C$ is a semidualizing module. After giving several cases in which different relative homologies agree, we use the Pontryagin duals of $\mathcal {G}_C$-projective modules to establish a balance result for such relative homology over a Cohen-Macaulay ring with a dualizing module $D$.
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참고문헌 (22)
참고문헌 신청
D. A. Jorgensen / 2012 / Presentations of rings with non-trivial semidualizing modules / Collect. Math 63 (2) : 165 ~ 180
D. D. Zhang / 2011 / Semidualizing modules and related modules / J. Algebra Appl 10 (6) : 1261 ~ 1282
D. White / 2010 / Gorenstein projective dimension with respect to a semidualizing module / J. Commut. Algebra 2 (1) : 111 ~ 137
E. E. Enochs / 2004 / Foxby equivalence and cotorsion theories relative to semi-dualizing modules / Math. Scand 95 (1) : 33 ~ 43
E. S. Golod / 1984 / G-dimension and generalized perfect ideals / Trudy. Mat. Inst. Steklov 165 : 62 ~ 66
D. D. Zhang / 2011 / Semidualizing modules and related modules / J. Algebra Appl 10 (6) : 1261 ~ 1282
D. White / 2010 / Gorenstein projective dimension with respect to a semidualizing module / J. Commut. Algebra 2 (1) : 111 ~ 137
E. E. Enochs / 2004 / Foxby equivalence and cotorsion theories relative to semi-dualizing modules / Math. Scand 95 (1) : 33 ~ 43
E. S. Golod / 1984 / G-dimension and generalized perfect ideals / Trudy. Mat. Inst. Steklov 165 : 62 ~ 66
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