Noncommutative Polynomial Relations
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چکیده
Terminology: We’ll say that two polynomials p, q are congruent, and write p ≡ q, if their equality is a consequence of our given relation. To be consistent, we also write the given relation as f ≡ 0. We must explain the consequences of f ≡ 0 specifically. They are that if u, v are any polynomials, then the product ufv is congruent to zero, as is a finite sum of such products. That is all. For instance, xy = 0 implies (yx)(xy)x + (x + y)(xy) = 0. It does not imply yx = 0.
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