Ring generated by binomial polynomials

From Commalg

This is a variation of polynomial ring
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Definition

Let be a commutative unital ring of characteristic zero. Let be the ring obtained by localizing at the multiplicative subset of nonzero integers. Then, the ring generated by binomial polynomials over is the subring of comprising all -linear combinations of the polynomials:

.

where (for , this is the constant polynomial ).

Equivalently, it is the tensor product with of the ring generated by binomial polynomials over the rational integers, i.e., the ring generated by binomial polynomials over .

Equivalently, it is the ring : the ring of all polynomials such that .

Facts