Weakly Standard Rings

The study of non-associative rings has yielded many interesting results in algebra. The special rings like weakly stand rings, in which the associative law is replaced by weak substitute, have applications in other branches of algebraic geometry,integration of analysis and algebra.In this work we present some identities of assosymmetric rings, antiflexible rings and weakly standard rings. In general, assosymmetric rings, antiflexible rings and rings with (x,y,x) and commutators in the left nucleus are not weakly standard rings.We prove that prime assosymmetric rings, antiflexible rings without non-zero nilpotent elements and semiprime rings with (x,y,x) and commutators in the left nucleus are weakly standard rings.We establish the structure of certain weakly standard rings.We prove associatativity,commutativity and nilpotency of weakly standard rings.Also we prove some properties of ideals in weakly standard rings.