Free algebra over a ring
that is associative and commutative
A free algebra in the variety of algebras over (see Rings and algebras). The elements of such a free algebra with a free generating system are linear combinations of elements of the free groupoid generated by with coefficients from . In other words, this free algebra is a free module over with the above-mentioned groupoid as its base. When is the ring of integers, a free algebra over is called a free ring (cf. Free associative algebra). A non-null subalgebra of a free algebra over a field is a free algebra.
Free algebra over a ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Free_algebra_over_a_ring&oldid=14483