Generalized Projective product of semi-rings

Abstract

The concept of Differential algebra has been played an influential role in various directions of abstract algebra. This notation has been considered before fifty years ago with semi-ring and several types of rings. Furthermore, the commutativity of a given ring or semi-ring has been also investigated under the notation of derivation and many studies have been published in this way. Based on the concept of derivation, its generalization has been introduced by Bresar [9] and a lot of works are presented about this generalization in various types of rings and semi-rings. Motivated by these works in the literature, we introduced the concept of generalized projective product of n-number of semi-rings. In addition, we studied the convers of this case which is saying that if the generalized projective product of n-number of semi-rings existed, then there exist a corresponding derivations, generalized derivations, semi-derivations, generalized semi-derivations, Jordan derivations, generalized Jordan derivations, Jordan semi-derivations and Generalized Jordan semi-derivations on the semi-rings  Ri respectively for any  i=1,2,..,k.