Construct the free algebra A over the ring R and the monoid M. The ring R may be any ring, while the monoid M may be a finitely presented semigroup, monoid, or group. The i-th generator may be referenced by the expression A.i, i = 1, ..., n, where n is the number of generators of M. Note that a special form of the assignment statement is provided which enables the user to assign names to the generators of A. In this form of assignment, the list of generator names is enclosed within angle brackets and appended to the variable name on the left hand side of the assignment statement.
> Z := Integers(); > M := FreeMonoid(2); > F := FreeAlgebra(Z, M);create the free algebra over the integers and the free monoid of rank 2. Here the generators may be referenced using the standard names, F.1 and F.2.
The statements
> K := GF(7); > M := Monoid<x, y | x^3 = 1, (x * y)^4 = 1>; > A<a, b> := FreeAlgebra(K, M);create the free algebra A over the finite field of three elements and the monoid M with two generators. The generators of A are assigned to the variables a and b.
The ring over which the algebra A is defined.
The monoid over which the algebra A is defined.[Next] [Prev] [Right] [Left] [Up] [Index] [Root]