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In mathematics, more specifically ring theory, a left, right or two-sided ideal of a ring is said to be a nil ideal if each of its elements is nilpotent. [1] [2]The nilradical of a commutative ring is an example of a nil ideal; in fact, it is the ideal of the ring maximal with respect to the property of being nil.
GameFAQs was started as the Video Game FAQ Archive on November 5, 1995, [10] by gamer and programmer Jeff Veasey. The site was created to bring numerous online guides and FAQs from across the internet into one centralized location. [11]
The nilradical of a commutative ring is the set of all nilpotent elements in the ring, or equivalently the radical of the zero ideal.This is an ideal because the sum of any two nilpotent elements is nilpotent (by the binomial formula), and the product of any element with a nilpotent element is nilpotent (by commutativity).
The nilpotent elements of a commutative ring R form an ideal of R, called the nilradical of R; therefore a commutative ring is reduced if and only if its nilradical is zero. Moreover, a commutative ring is reduced if and only if the only element contained in all prime ideals is zero. A quotient ring R/I is reduced if and only if I is a radical ...
The first wire says "2,2" place the wire where the 2ND column and the 2ND row connects. If the second one says "4,1", place the wire where the 4Th column (on top) and the 1st row connect. Please ...
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
Bradley Lamar Colburn (born February 10, 1987), [3] better known by his online alias theRadBrad, is an American YouTuber and Let's Player most notable for his video game walkthroughs of various new games. [4] [5] [6] He has been interviewed by various publications since becoming active in 2010.
In algebra, the nilradical of a Lie algebra is a nilpotent ideal, which is as large as possible. The nilradical n i l ( g ) {\displaystyle {\mathfrak {nil}}({\mathfrak {g}})} of a finite-dimensional Lie algebra g {\displaystyle {\mathfrak {g}}} is its maximal nilpotent ideal , which exists because the sum of any two nilpotent ideals is nilpotent.