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Relative tilting modules with respect to a semidualizing module

Maryam Salimi (2019)

Czechoslovak Mathematical Journal

Let R be a commutative Noetherian ring, and let C be a semidualizing R -module. The notion of C -tilting R -modules is introduced as the relative setting of the notion of tilting R -modules with respect to C . Some properties of tilting and C -tilting modules and the relations between them are mentioned. It is shown that every finitely generated C -tilting R -module is C -projective. Finally, we investigate some kernel subcategories related to C -tilting modules.

Restricted homological dimensions over local homomorphisms and Cohen-Macaulayness

Fangdi Kong, Dejun Wu (2018)

Czechoslovak Mathematical Journal

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.

Rings with divisibility on descending chains of ideals

Oussama Aymane Es Safi, Najib Mahdou, Ünsal Tekir (2024)

Czechoslovak Mathematical Journal

This paper deals with the rings which satisfy D C C d 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...

Testing flatness and computing rank of a module using syzygies

Oswaldo Lezama (2009)

Colloquium Mathematicae

Using syzygies computed via Gröbner bases techniques, we present algorithms for testing some homological properties for submodules of the free module A m , where A = R[x₁,...,xₙ] and R is a Noetherian commutative ring. We will test if a given submodule M of A m 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 A m and also an algorithm that computes the projective dimension of an arbitrary submodule...

When every flat ideal is projective

Fatima Cheniour, Najib Mahdou (2014)

Commentationes Mathematicae Universitatis Carolinae

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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