• There is no "natural" way to define the tensor product of two representations of an associative algebra.
• Sergei Arkhipov on 2-, 3- and n-structures à la Baez & Co.
• Grothendieck's contributions by sowa
• Condition for an element of the exterior algebra to be decomposable are described by Plücker relations
• Deformation property of Koszul algebras by Leonid Positselski
• (Finite-dimensional?) modules over K[t]/(t²) are exactly Kⁿ ⊕ (K[t]/(t²))^m for nonnegative integers n, m.

Gröbner bases computations

• GAP: GBNP - package for (noncommutative) Gröbner bases.
  Example of (commutative) Gröbner base computation:

  x := Indeterminate (Rationals, "x");     
  y := Indeterminate (Rationals, "y");
  z := Indeterminate (Rationals, "z");
  GroebnerBasis ([x^2+y^2+z^2-1, x^2+z^2-y, x-y], MonomialLexOrdering());
  

• Bergman [public domain]. LISP-based.
• CoCoA
• Macauley2: among associative noncommutatiuve rings, only some very special types are supported.
• Sage
• SALSA
• Singular: arguably the best choice for commutative Gröbner bases.
  Example of (commutative) Gröbner base computation:

  ring R = 0, (x,y,z), lp;
  ideal I = x^2+y^2+z^2-1, x^2+z^2-y, x-y;
  std (I);
  

  Plural.
• Gröbner bases implementations in various systems.
• Gröbner bases bibliography
• Haskell implementation of algorithms of Dotsenko-Khoroshkin for building a Gröbner base for operad by Mikael Vejdemo Johansson.
  Examples: [Mikael Vejdemo Johansson's blog] [A173990 from OEIS (Dotsenko)]