| 21. | So, let be a unique factorization domain, which is not a field, and the univariate polynomial ring over.
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| 22. | He was a first-class contract bridge player and wrote about bridge and other games, including ideals of polynomial rings.
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| 23. | Although developed independently, it may also be seen as the instantiation of Knuth Bendix algorithm in the theory of polynomial rings.
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| 24. | Mathematical objects such as vector spaces and polynomial rings can be carried over into these new theories by mimicking their abstract properties.
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| 25. | This is for instance the case when considering a monomial basis of a polynomial ring, or a monomial ordering of that basis.
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| 26. | The first algorithm for computing primary decompositions for polynomial rings over a field of characteristic 0 was published by Noether's student.
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| 27. | A classical example in nineteenth century was the extensive study ( in particular by ideal inside the polynomial ring generated by the invariants.
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| 28. | He received his PhD from Leningrad University in 1974; his thesis was titled " Projective modules over polynomial rings ".
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| 29. | The analogous conjecture with the integers replaced by the one-variable polynomial ring over a finite field is " false ".
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| 30. | This statement goes back to David Hilbert's foundational work on homological properties of polynomial rings, see Hilbert's syzygy theorem.
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