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Non-commutative rings and algebras, non-associative algebras. Can be used in combination with ra.rings-and-algebras

3 votes
3 answers
2k views

How to work with co-multiplication?

Let $C$ be a coalgebra and $\Delta: C \to C\otimes C$ a co-multiplication map. Then, due the co-associative property we can consider $\Delta^m$. But how is defined $\Delta^{m}: C \to C^{\otimes m}$? G …
Binai's user avatar
  • 829
4 votes
3 answers
559 views

Gröbner/SAGBI bases for non-commutative setting

It is well known that SAGBI/Gröbner bases are important for commutative and non-commutative algebra. The references for commutative scenery is ample and vast, but I am in trouble to find a good refere …
Binai's user avatar
  • 829
21 votes
4 answers
7k views

Binomial Expansion for non-commutative setting

What could be a reference about binomial expansions for non-commutative elements? Specifically, where can I find a closed formula for the expansion of $(A+B)^n$ where $[A,B]=C$ and $[C,A]=[C,B]=0$? …
Binai's user avatar
  • 829