Characterizing skew n-derivations on triangular rings

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Abstract

Every ring containing a unity has a maximal right ring of quotients. In this paper, we investigate a skew n-derivation ϕ on a class of triangular rings and use the theory of maximal right ring of quotients to demonstrate that ϕ is an extremal skew n-derivation. This result not only significantly generalizes previous findings on derivations, but also forges a strong connection between the theory of derivations and that of rings of quotients, providing a tool for characterizing functional identities in various specific operator algebras.

Keywords

triangular ring / skew 3-derivation / skew n-derivation / maximal right ring of quotients / extremal skew n-derivation

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