Abstract
In Chapter 4, we used ultraproducts to derive uniform bounds for various algebraic operations, where the bounds are given in terms of the degrees of the polynomials involved. This was done by constructing a faithfully flat embedding of the polynomial ring A into an ultraproduct U(A) of polynomial rings, called its ultra-hull. Moreover, A is characterized as the subring of U(A) of all elements of finite degree. In this chapter, we want to put these uniformity results in a more general context, by replacing the degree on A by what we will call a proto-grading.
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Schoutens, H. (2010). Protoproducts. In: The Use of Ultraproducts in Commutative Algebra. Lecture Notes in Mathematics(), vol 1999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13368-8_9
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DOI: https://doi.org/10.1007/978-3-642-13368-8_9
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