【摘要】 Ardizzoni,Brzeziński和Menini在研究代数的形式光滑性以及形式光滑双模时利用相对右导出函子引入了模-相对Hochschild上同调的概念.本文利用相对左导出函子相应地给出模-相对Hochschild同调的定义,讨论了在Morita型稳定等价下,代数的Hochschild(上)同调、相对Hochschild(上)同调以及模-相对Hochschild(上)同调三者之间的关系,证明了模-相对Hochschild同调与上同调是Morita型稳定等价下的不变量.作为该结果的应用,我们得到形式光滑双模与可分双模的一种构造方法,并给出了通常意义下的Hochschild(上)同调是Morita型稳定等价不变量的一种新的证明.更多还原

【Abstract】 Based on the theory of relative right derived functors, module-relative-Hochschild cohomology was introduced by Ardizzoni, Brzezin′ski and Menini when they studied the formal smoothness. In this paper, we introduce the module-relative-Hochschild homology using relative left derived functors, discuss the relations of Hochschild (co)homology, relative Hochschild (co)homology and module-relative-Hochschild (co)homology under stable equivalences of Morita type, and prove that module-relative-Hochschild homology and cohomology are invariants under stable equivalences of Morita type. As a consequence, we get a method of constructing formally smooth bimodules and separable bimodules, and give a new proof to the known fact that the stable equivalence of Morita type preservers the ordinary Hochschild (co)homology.更多还原