Soumia Mamdouhi | Searcharxiv

arXiv2024

A new approach to flatness in categories of sheaves

Recently, many authors have embraced the study of certain properties of modules such as projectivity, injectivity and flatness from an alternative point of view. This way, Durgun has introduced absolutely pure domains of modules as a mean to gauge the extent of the flatness of any given module (so not just to determine whether or not the module is flat). In this paper, we develop a new treatment of the goemetric flatness in categories of sheaves which shed more light on some of its various important aspects. Namely, in terms of this new approach, some classical schemes are characterized, some new results are established and also known ones are generalized.

math.AG↗

arXiv2021

n-gr-Coherent rings and Gorenstein graded modules

Let R be a graded ring and n > 1 an integer. In this paper, We introduce the notions of Ding n-gr-injective and Ding n-gr-flat modules by using of special finitely presented graded modules . Then, some properties of Ding n-gr-injective and Ding n-gr-flat modules are obtained. On n-gr-coherent rings, we investigate the relationships among Ding n-gr-injective and Ding n-gr-flat modules and also, we prove that any graded module in R-gr (resp. gr-R) admits an Ding n-gr-injective (resp. Ding n-gr-flat) cover and preenvelope.

math.RA↗