Rings over JR-2CN and JR-3CN
Rand Alfaris, Hailiza Kamarulhaili · AIP conference proceedings · 2012
Constructing rings based on the families of summations of two and three signed cubic numbers, JR-2CN and JR-3CN, is one of the main goals in this research. Rings whose elements are ordered pairs that based on the Abelian groups JR-2CN and JR-3CN is introduced. Two new multiplicative operations have been defined to be associated with the Abelian groups JR-2CN and JR-3CN respectively to form a ring. Through studying the properties of these rings, subrings and ideals have been defined and introduced. As an implementation, Isomorphism has been defined between the two rings, and in addition to this, polynomial ring has been also defined for each family.