arXiv subjects

Abolfazl Tarizadeh

Publications and source records attributed to Abolfazl Tarizadeh.

38 records · Page 3Linked to original sources

arXiv2016

Gabriel localization theory and its applications

In this article first we develop the Gabriel localizations (abbreviated as G-localizations) for commutative rings, specially some new results in this direction are proven. Then, as an application, it is shown that a ring map is a flat epimorphism if and only if it corresponds to a kind of the G-localizations. As a by-product of this study, a characterization for the flatness of the quotient rings is given. The exactness of the G-localization functor are characterized. The structure of prime ideals in the G-localization rings are also studied. Finally, it is shown that the Gabriel localization theory is a natural generalization of the usual localization theory.

math.AC↗

arXiv2012

On the category of profinite spaces as a reflective subcategory

In this paper by using the ring of real-valued continuous functions $C(X)$, we prove a theorem in profinite spaces which states that for a compact Hausdorff space $X$, the set of its connected components $X/_{\sim}$ endowed with some topology $\mathscr{T}$ is a profinite space. Then we apply this result to give an alternative proof to the fact that the category of profinite spaces is a reflective subcategory in the category of compact Hausdorff spaces. Finally, under some circumstances on a space $X$, we compute the connected components of the space $t(X)$ in terms of the ones of the space $X$.

math.AC↗