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The Baer radical of a ring is the intersection of the prime ideals of the ring R. Equivalently it is the smallest semiprime ideal in R. The Baer radical is the lower radical of the class of nilpotent rings. Also called the "lower nilradical" (and denoted Nil ∗ R), the "prime radical", and the "Baer-McCoy radical".
For a general ring with unity R, the Jacobson radical J(R) is defined as the ideal of all elements r ∈ R such that rM = 0 whenever M is a simple R-module.That is, = {=}. This is equivalent to the definition in the commutative case for a commutative ring R because the simple modules over a commutative ring are of the form R / for some maximal ideal of R, and the annihilators of R / in R are ...
Amazon acquired the global television rights for J. R. R. Tolkien's The Lord of the Rings (1954–55) in November 2017. The company's streaming service, Prime Video, gave a multi-season commitment to a series based on the novel and its appendices, to be produced by Amazon Studios in association with New Line Cinema and in consultation with the Tolkien Estate. [1]
The Lord of the Rings: The Rings of Power is an American fantasy television series developed by J. D. Payne and Patrick McKay for the streaming service Amazon Prime Video.It is based on J. R. R. Tolkien's history of Middle-earth, primarily material from the appendices of the novel The Lord of the Rings (1954–55).
Consider the ring of integers.. The radical of the ideal of integer multiples of is (the evens).; The radical of is .; The radical of is .; In general, the radical of is , where is the product of all distinct prime factors of , the largest square-free factor of (see Radical of an integer).
On November 21, a series of bonus segments called "The Making of The Rings of Power" were added to Prime Video's X-Ray feature, allowing viewers to learn additional information about the series while watching it. X-Ray executive Craig Muller said the segments were created from thousands of hours of behind-the-scenes footage.
Season 2 of The Rings of Power is scoring well with fans on Rotten Tomatoes.Compared to Season 1’s 38% “fresh” rating (with 25,000-plus reviews), the first three episodes are currently ...
A ring R is called a Jacobson ring if the nilradical and Jacobson radical of R/P coincide for all prime ideals P of R. An Artinian ring is Jacobson, and its nilradical is the maximal nilpotent ideal of the ring. In general, if the nilradical is finitely generated (e.g., the ring is Noetherian), then it is nilpotent.