Motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study Lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎It is shown‎ ‎that every Lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎The definition of Lie $n$-higher‎ ‎derivations on operator algebras and related pot...

Let K be a field having prime characteristic p. The following conditions on a subfield k of K are equivalent: (i) || K" (k) = k and K/k is separable, (ii) k is the field of constants of an infinite higher derivation defined in K. (iii) k is the field of constants of a set of infinite higher derivations defined in K. If K/k is separably generated and k is algebraically closed in K, then k is the...

Much of the wonderful invariant theory of the 19 century worked over fields of characteristic zero, while the theory for prime characteristic lagged behind. However, the Frobenius (p power) map in characteristic p > 0 leads to a rich theory of invariants in prime characteristic. This theory is closely bound up with the Steenrod Algebra, which allows us to derive new invariants from known invari...

we show that  higher derivations on a hilbert$c^{*}-$module associated with the cauchy functional equation satisfying generalized hyers--ulam stability.

motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎it is shown‎ ‎that every lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎the definition of lie $n$-higher‎ ‎derivations on operator algebras and related pote...