| 1. | Skew polynomial rings are closely related to crossed product algebras.
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| 2. | Polynomial rings and their quotients by homogeneous ideals are typical graded algebras.
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| 3. | Polynomial rings over the integers or over a field are unique factorization domains.
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| 4. | Matrices over a polynomial ring are important in the study of control theory.
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| 5. | The substitution is a special case of the universal property of a polynomial ring.
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| 6. | Note that unlike in an actual polynomial ring, the variables do not commute.
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| 7. | Complex reflection groups arise in the study of the invariant theory of polynomial rings.
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| 8. | The ring of power series can be seen as the completion of the polynomial ring.
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| 9. | Every ideal in a polynomial ring.
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| 10. | Therefore, the remainder of this article will be restricted to the quotients of polynomial rings by ideals.
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