Homological dimensions and regular rings

A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.Comment: 8 page

Investigation of charges-driven interactions between graphene and different SiO2 surfaces

As being only one atom thick, most of the device applications require graphene to be partially or fully supported by a substrate, which is typically silicon dioxide (SiO2). According to a common understanding, graphene interacts with SiO2 through weak, long-range van der Waals forces, emerging between instantaneous/induced dipoles, in contrast to the experimental evidence that reveals a surprisingly high interaction between graphene and SiO2. In order to get further insight into this phenomenon, we carried out diverse physical measurements on SiO2 substrates, prepared via different fabrication protocols, with and without graphene on top. As a result, the role of the oxide surface charges is recognized for the first time as a main factor causing graphene to strongly interact with SiO2. Our findings provide guidelines for designing 2D materials interaction with a substrate through modulation of surface charges. This, in turn, can facilitate the development of new graphene based microelectronic devices