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 …

2023年3月25日 · Every alternative or special Jordan nil ring of bounded index and without elements of order 2 in the additive group is locally nilpotent (Shirshov's theorem). A finite …

2020年6月6日 · An ideal of $ R $ is a nil ideal if it is a nil subset. There is a largest nil ideal, which is called the nil radical. One has that. $$ \mathop {\rm Jac} ( R) \supset \textrm { Nil Rad } ( R) …

2024年8月19日 · You will be able to find nil ideals and nilradicals discussed in absolutely any commutative algebra book... the set of nilpotent elements of a ring in general don't have to …

In mathematics, the word null (from German: null[citation needed] meaning "zero", which is from Latin: nullus meaning "none") is often associated with the concept of zero, or with the concept …

The set of all positive integers will be denoted by N. For n ∈ N we denote by Pn the set of all complex polynomials in n non-commuting variables. De nition 1. Let A be a Banach algebra. …

An element x x of a ring is nilpotent if xn = 0 x n = 0 for some positive integer n n. A ring R R is nil if every element in R R is nilpotent. Similarly, a one- or two-sided ideal is called nil if each of its …

2018年2月1日 · I was given the exercise to show that Nil (Nil ($R$) = Nil ($R$), where $R$ is a ring. Is $x \in$ Nil (Nil ($R$)) equivalent to $\exists n, m$ s.t. $x^ {n^m}=0$? I am having a bit …

A Lie algebra $ {\mathfrak g}$ over a field $k$ is called nil if there is a function $n: {\mathfrak g}\times {\mathfrak g}\to {\mathbb N}$ such that $ ( {\rm ad}\; x)^ {n (x,y)} (y) = 0$, where $ ( …

2017年12月30日 · Let R R be a ring, A A be a nil left ideal, B B be a nil ideal. Prove that A + B A + B is a left nil ideal. (Nil ideal is an ideal where every element is nilpotent.) Generally, the sum …