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Results tagged with derivations
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user 16537
A derivation on a ring 𝑅 is a map 𝐷:𝑅→𝑅 satisfying 𝐷(𝑎+𝑏)=𝐷(𝑎)+𝐷(𝑏) and 𝐷(𝑎𝑏)=𝑎𝐷(𝑏)+𝐷(𝑎)𝑏.
1
vote
Reference for a certain derivation on the ring of ordered series over a free monoid
Following Benjamin Steinberg's advice (in the comments under the OP), I contacted Christophe Reutenauer, who pointed out that the derivation $\partial_z$ in the OP is, of course, well known and its fi …
- 10.5k
5
votes
1
answer
86
views
Reference for a certain derivation on the ring of ordered series over a free monoid
Let $R$ be a (commutative or non-commutative) unital ring, $X$ be a non-empty set, and $R \langle\! \langle X \rangle\! \rangle$ be the ordered series ring (in fact, a ring of formal power series over …
- 10.5k
5
votes
Accepted
What is the derivative of $1/g$ in a differential semiring?
(iv) The set $\mathcal D(S)$ of all derivations on a (commutative or non-commutative) semiring $S$ is naturally made into a left/right $S$-semimodule, by endowing it with the operation of pointwise addition …
- 10.5k