in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of R is isomorphic to Z_2 and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.

Substitution of two or four carbon atoms by nitrogen in the corannulene molecule as a carbon nanostructure was done and the obtained structures were optimized at MP2/6-31G(d) level of theory. Calculations of the nucleus-independent chemical shift (NICS) were performed to analyze the aromaticity of the corannulene rings and its derivatives upon doping with N at B3LYP/6-31G(d) level of theory. Re...