The effect of nucleus size on the electron energy levels: via Seiberg-Witten map

We compare the effects of the entering non - commutative geometry in physics, which have studied by Bob's shift method and Seiberg-Witten map. Due to the corrections of the electron energy levels, we demonstrate that two approaches are not equivalent. We show that the electric and magnetic dipole moments, as well as one loop vertex correction, change due to the mapping selection. Furthermore, we provide a way to communicate the results of the two methods.Comment: 3 pages, 0 figure

Electrodynamics in Non-commutative Curved Space Time

We study the issue of the electrodynamics theory in noncommutative curved space time (NCCST) with a new star-product. In this paper, the motion equation of electrodynamics and canonical energy-momentum tensor in noncommutative curved space time will be found. The most important point is the assumption of the noncommutative parameter ($\theta$) be x^{\m}-independent.Comment: 7 page

On Shimura subvarieties of the Prym locus

We show that families of Pryms of abelian Galois covers of $\mathbb{P}^1$ in $A_{g-1}$ (resp. $A_g$) do not give rise to high dimensional Shimura subvareties.Comment: 12 page

On finite type epimorphisms of rings

In this note, finite type epimorphisms of rings are characterized.Comment: 5 page

Tensor of the energy - momentum and forbiddance of the classical Lump

We show that the static solutions of massive classical fields are forbidden in the Minkowski space time with dimensions higher than $2$. The purpose of this study is to generalize the forbiddance of the time independent localized classical fields in general space time. We generalize the Derrick theorem as unstable stationary localized solutions for the nonlinear wave equation or the nonlinear Klein - Gordon equation in Minkowski space time. Our approach employs the tensor of the energy - momentum based on Weber's method. We exploite the Bateman - Caldilora - Kanai model and the Deser method for the research of the Yang - Mills Lumps as massive solutions. We also use Riemann's coordinates for parametrization of tangent space as a local framework. The important point of this article is the homomorphism between the Minkowsian and pseudo Riemann's manifolds.Comment: 7 page

Notes on finitely generated flat modules

In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a finitely many minimal primes or a finitely many maximal ideals then every finitely generated flat module over it is projective. It is also shown that if a particular subset of the prime spectrum of a ring satisfies some certain ascending or descending chain conditions then every finitely generated flat module over this ring is projective. These results generalize some major results in the literature on the projectivity of finitely generated flat modules.Comment: 9 pages. arXiv admin note: substantial text overlap with arXiv:1701.0773

On the idempotents of commutative rings

In this paper, the Chinese Remainder Theorem is proved by a simple and short approach. The method of the proof is constructive and so gives us a formula to compute all of the idempotents of an Artinian ring, specially $\mathbb{Z}/m\mathbb{Z}$, in an explicit way. A new result on the lifting idempotents is also obtained.Comment: 5 page

Abstract sheaf theory

In this article, the theory of sheaves is studied from a categorical point of view. This perspective vastly generalizes the usual theory of sheaves of sets to a more abstract setting which allows us to investigate the theory of sheaves with values in an arbitrary category.Comment: 28 page

Rational points on abelian varieties over function fields and Prym varieties

In this paper, using a generalization of the notion of Prym variety for covers of quasi-projective varieties, we prove a structure theorem for the Mordell-Weil group of the abelian varieties over function fields that are twists of Abelian varieties by Galois covers of irreducible quasi-projective varieties. In particular, the resutls we obtain contribute in the construction of Jacobians (of covers of the projective line) of high rank.Comment: 6 pages, comments are welcome

Non-commutativity on another Minkowski space-time: Vierbein formalism and Higgs approach

We extend the non-commutative coordinates relationship into other than the Minkowski space-time. We clarify the non-commutativity dependency to the geometrical structure. As well as, we find an inverse map between Riemann's normal and global coordinates. Furthermore, we show that behavior of the corresponding coordinates non-commutativity like as a tensor. All results summarized for the Schwarzschild metric. And they summarized for the space-time in the presence of weak gravitational waves.Comment: 4 pages, 0 figur