Let [Formula: see text] be a ring, class of text]-modules and an integer. We introduce the concepts Gorenstein text]-[Formula: text]-injective text]-flat modules via special finitely presented modules. Besides, we obtain some equivalent properties these on text]-coherent rings. Then investigate relations among text]-injective, text]-flat, injective flat text]-rings (i.e., self rings). Several k...

1 Parameters The paper presents the first attempt to estimates the ILC damping ring impedance and compare thresholds of the classical instabilities for several designs initially proposed for the DR. The work was carried out in the spring of 2006. Since then the choice of the DR is narrowed. Nevertheless, the analysis described below may be useful for the next iterations of the beam stability. W...

Coherent Synchrotron Radiation (CSR) can play an important role by not only increasing the energy spread and emittance of a beam, but also leading to a potential instability. Previous studies of the CSR induced longitudinal instability were carried out for the CSR impedance due to dipole magnets. In this paper, the instability due to the CSR impedance from a wiggler is studied assuming a large ...

Let R be a commutative ring with identity and let M an R-module which is generated by μ elements but not fewer. We denote SLn(R) the group of n×n matrices over determinant 1. En(R) subgroup differ from single off-diagonal coefficient. Given n≥μ G∈{SLn(R),En(R)}, we study action G matrix right-multiplication on Vn(M), set Mn whose components generate M. Assuming that finitely presented elementar...

In this note, we characterize the (weak) Gorenstein global dimension for arbitrary associative rings. Also, we extend the well-known Hilbert’s syzygy Theorem to the weak Gorenstein global dimension, and we study the weak Gorenstein homological dimensions of direct product of rings which gives examples of non-coherent rings with finite Gorenstein dimensions > 0 and infinite classical weak dimens...