Transfer of homological properties under base change is a classical field of study. Let $Rightarrow S$ 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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机译：在碱基变化下同源性的转移是一个经典的研究领域。令$ R rightarrow S $为环同态。考虑$ Ltp {U} {X} $（或$ RHom {X} {U} $）和$ X $之间无界复合物的Gorenstein射影（或Gorenstein内射）维度的关系，其中$ X $ $ R $复数和$ U $是$ S $复数。此外，给出了一些充分的条件，在这些条件下，等式$ Gdimm（ Ltp {U} {X}）= Gdim {X} + pd {U} $和$ Gidd（ RHom {X} {U }）= Gdim {X} + id {U} $保留。
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