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Let be a commutative Noetherian ring, and let be a semidualizing -module. The notion of -tilting -modules is introduced as the relative setting of the notion of tilting -modules with respect to . Some properties of tilting and -tilting modules and the relations between them are mentioned. It is shown that every finitely generated -tilting -module is -projective. Finally, we investigate some kernel subcategories related to -tilting modules.
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...
Using syzygies computed via Gröbner bases techniques, we present algorithms for testing some homological properties for submodules of the free module , where A = R[x₁,...,xₙ] and R is a Noetherian commutative ring. We will test if a given submodule M of is flat. We will also check if M is locally free of constant dimension. Moreover, we present an algorithm that computes the rank of a flat submodule M of and also an algorithm that computes the projective dimension of an arbitrary submodule...
In this paper, we study the class of
rings in which every flat ideal is
projective. We investigate the stability
of this property under homomorphic image,
and its transfer to various contexts
of constructions such as direct products,
and trivial ring extensions. Our results
generate examples which enrich the
current literature with new and original
families of rings that satisfy this
property.
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