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Transfer of homological properties under base change is a classical field of study. Let $R\rightarrow S$ be a ring homomorphism. The relations of Gorenstein projective (or Gorenstein injective) dimensions of unbounded complexes between $\Ltp{U}{X}$ (or $\RHom{X}{U}$) and $X$ are considered, where $X$ is an $R$-complex and $U$ is an $S$-complex. In addition, some sufficient conditions are given under which the equalities $\Gdimm(\Ltp{U}{X})=\Gdim{X}+\pd{U}$ and $\Gidd(\RHom{X}{U})=\Gdim{X}+\id{U}$ hold.
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참고문헌 (12)
참고문헌 신청
J. Asadollahi / 2006 / Gorenstein injective dimension for complexes and Iwanaga-Gorenstein rings / Comm. Algebra 34(8):3009~3022
L. L. Avramov / 1991 / Homological dimensions of unbounded complexes / J. Pure Appl. Algebra 71(2-3):129~155
L. W. Christensen / 2000 / Gorenstein Dimensions / Lecture Notes in Math 1747
L. W. Christensen / 2006 / On Gorenstein projective, injective and flat dimensions—A functorial description with applications / J. Algebra 302(1):231~279
L. W. Christensen / 2009 / Ascent properties of Auslander categories / Canad. J. Math 61(1):76~108
L. L. Avramov / 1991 / Homological dimensions of unbounded complexes / J. Pure Appl. Algebra 71(2-3):129~155
L. W. Christensen / 2000 / Gorenstein Dimensions / Lecture Notes in Math 1747
L. W. Christensen / 2006 / On Gorenstein projective, injective and flat dimensions—A functorial description with applications / J. Algebra 302(1):231~279
L. W. Christensen / 2009 / Ascent properties of Auslander categories / Canad. J. Math 61(1):76~108
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