Some functors related to polynomial theory. II
Forms and mappings. I: Generalities
Relations between Elements r²-r
We prove that generating relations between the elements [r] = r²-r of a commutative ring are the following: [r+s] = [r]+[s]+rs[2] and [rs] = r²[s]+s[r].
Relations between Elements and p·1 for a Prime p
For any positive power n of a prime p we find a complete set of generating relations between the elements [r] = rⁿ - r and p·1 of a unitary commutative ring.
Algebraic and geometric approach to the classification of semispaces.
On n-derivations and Relations between Elements rⁿ-r for Some n
We find complete sets of generating relations between the elements [r] = rⁿ - r for and for n = 3. One of these relations is the n-derivation property [rs] = rⁿ[s] + s[r], r,s ∈ R.
On the shape of n-derivations
We present some classification results for n-derivations over certain commutative rings.
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