ABSTRACT
This chapter essentially shows that some notions of Commutative Algebra, as noetherianity or primary decomposition, can be studied in some classes of commutative nonassociative rings. The class C that consists of commutative power-associative rings U of prime characteristic p > 0 such that the map U → U defined by x → xp is a ring homomorphism and the image is contained in the associative nucleus N(U). The chapter shows applying the results in the study of alternative rings of characteristic 3 and Jordan and Moufang rings of characteristic 2. Zhevlakov’ ideas are followed in studying alternative rings with finiteness conditions.
