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In this note, for a ring endomorphism and an -derivation of a ring , the notion of weakened -skew Armendariz rings is introduced as a generalization of -rigid rings and weak Armendariz rings. It is proved that is a weakened -skew Armendariz ring if and only if is weakened -skew Armendariz if and only if is weakened -skew Armendariz ring for any positive integer .
Commutative rings over which no endomorphism algebra has an outer automorphism are studied.
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