Commutativity and Standard Polynomial Identities in τ ‐Prime Rings With n ‐Antihomoderivations

This paper studies the effect of n ‐antihomoderivations on τ ‐prime rings. The first part establishes commutativity criteria by imposing natural commutator, centralizing, Lie‐type, and Jordan‐type identities on a nonzero τ ‐ideal. The second part investigates when centralizing conditions on the action of the n ‐antihomoderivation on τ ‐symmetric elements ensure that the ring satisfies the standard identity S ₄ . Thus, the paper contains two related but distinct contributions: commutativity results in the first part and an S ₄ result in the second part.