DERIVATION ON SEVERAL RINGS - Thomas, Abdiel Bellamy; Puspita, Nikken Prima; Fitriani, Fitriani (PATTIMURA UNIVERSITY, 2024)
Research on ring derivation is one of the studies that is quite popular among algebra lovers. The definition of the derivation on the ring is motivated by the derivation in calculus which has Leibniz's rule. The purpose of this paper is to show some of the derivation properties on several rings, namely divisor rings, cartesian product rings, and factor rings. Let be a commutative ring with multiplicative identity and A the set of multiplicative closed that has non-zero divisor. In this paper, we have shown some results of derivation on ring theory. If is a ring derivation of R and is a divisor ring of , we can construct for all , then the map is a derivation on . The concept of embedding one ring into another ring can be used so that the ring of constant of , namely , is a subring of the divisor ring . Related to the ideal on ring theory, if I is an ideal of R, then where is also a derivation on the ring . The last result in this paper comes from the ring of cartesian product, take be a ring with derivation for . The cartesian product ring have a derivation ring defined by for any .