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The Lord of the Rings: The Rings of Power premiered on September 1, 2022. The first season was released through October and was the most-watched of any Prime Video original series according to Amazon. It received generally positive reviews from critics, particularly for its visuals and designs, but there were criticisms for the writing and pacing.
Every field is a Henselian local ring. (But not every field with valuation is "Henselian" in the sense of the fourth definition above.) Complete Hausdorff local rings, such as the ring of p-adic integers and rings of formal power series over a field, are Henselian. The rings of convergent power series over the real or complex numbers are Henselian.
3. An analytic ring is a quotient of a ring of convergent power series in a finite number of variables over a field with a valuation. analytically This often refers to properties of the completion of a local ring; cf. #formally 1. A local ring is called analytically normal if its completion is an integrally closed domain. 2.
The Weierstrass preparation theorem can be used to show that the ring of convergent power series over the complex numbers in a finite number of variables is a Wierestrass ring. The same is true if the complex numbers are replaced by a perfect field with a valuation.
Quotient rings of the ring are used in the study of a formal algebraic space as well as rigid analysis, the latter over non-archimedean complete fields. Over a discrete topological ring, the ring of restricted power series coincides with a polynomial ring; thus, in this sense, the notion of "restricted power series" is a generalization of a ...
Nielsen Media Research, which records streaming viewership on US television screens, estimated that The Rings of Power was the most-watched original streaming series for the week of its premiere with 1.02 billion minutes viewed in its first four days. This was below Nielsen's estimation for the first season's initial four days (1.25 billion ...
Titled Deadline's Inside the Ring: LOTR: The Rings of Power, a new episode of the aftershow was released soon after each episode of The Rings of Power debuted on Prime Video. The aftershow features interviews with cast and crew as well as exclusive "footage and insights" for each episode. [346]
A formal power series can be loosely thought of as an object that is like a polynomial, but with infinitely many terms.Alternatively, for those familiar with power series (or Taylor series), one may think of a formal power series as a power series in which we ignore questions of convergence by not assuming that the variable X denotes any numerical value (not even an unknown value).