# dendriform

## Definitions

• WordNet 3.6
• adj dendriform resembling a tree in form and branching structure "arborescent coral found off the coast of Bermuda","dendriform sponges"
• ***
Webster's Revised Unabridged Dictionary
• a Dendriform Resembling in structure a tree or shrub; having a branching shape.
• ***
Century Dictionary and Cyclopedia
• dendriform Resembling a tree; tree-like in form; arborescent; dendritic. Also dendritiform.
• ***
Chambers's Twentieth Century Dictionary
• adj Dendriform den′dri-form having the appearance of a tree.
• ***

## Etymology

Webster's Revised Unabridged Dictionary
Gr. de`ndron tree + -form,
Chambers's Twentieth Century Dictionary
Formed from Gr. dendron, a tree, and L. forma, form.

## Usage

### In literature:

It is not a pair of simple tubes, nor of dendriform tubes, but a closed network.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 3" by Various
Tracheae are developed which are dendriform and with spiral thickening of their lining.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 6" by Various
***

### In science:

By this theorem, all dendriform dialgebra (resp. trialgebra) structures on V could be recovered from O-operators on the module (resp. on the algebra).
O-operators on associative algebras and dendriform algebras
Let (V, ≺, ≻, ·) be a dendriform trialgebra.
O-operators on associative algebras and dendriform algebras
Then it is straightforward to check that the dendriform trialgebra axioms of (V, ≺, ≻, · ) imply that (V, ·, L≻ , R≺ ) satis ﬁes all the axioms in Eq. (6) – (8) for a ( V, ∗)-bimodule k-algebra.
O-operators on associative algebras and dendriform algebras
Let (A, ≺, ≻, ·) be a dendriform trialgebra.
O-operators on associative algebras and dendriform algebras
Guo, Rota-Baxter algebras and dendriform algebras, J.
O-operators on associative algebras and dendriform algebras
***