Resolutions and lattices.
We define and study restricted projective, injective and flat dimensions over local homomorphisms. Some known results are generalized. As applications, we show that (almost) Cohen-Macaulay rings can be characterized by restricted homological dimensions over local homomorphisms.
This paper deals with the rings which satisfy condition. This notion has been introduced recently by R. Dastanpour and A. Ghorbani (2017) as a generalization of Artnian rings. It is of interest to investigate more deeply this class of rings. This study focuses on commutative case. In this vein, we present this work in which we examine the transfer of these rings to the trivial, amalgamation and polynomial ring extensions. We also investigate the relationship between this class of rings and the...