On the tensor product of polynomials over a ring
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Given polynomials a and b over an integral domain R, their tensor product (denoted a ⊗ b) is a polynomial over R of degree deg(a) deg(b) whose roots comprise all products αβ, where α is a root of a, and β is a root of b. This paper considers basic properties of ⊗ including how to factor a ⊗ b into irreducibles factors, and the direct sum decomposition of the ⊗-product of fields.
Glasby, S. P. (2001). On the tensor product of polynomials over a ring. Journal of the Australian Mathematical Society, 71(3), 307–324. https://doi.org/10.1017/s1446788700002950
Journal of the Australian Mathematical Society