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# nilpotent

## Definitions

### from The American Heritage® Dictionary of the English Language, 4th Edition

• n. An algebraic quantity that when raised to a certain power equals zero.

### from Wiktionary, Creative Commons Attribution/Share-Alike License

• adj. Describing an element, of a ring, for which there exists some positive integer n such that xn = 0.

### from The Century Dictionary and Cyclopedia

• In mathematics, vanishing on being raised to a certain power. Thus, if i be such an expression in multiple algebra that i × i × i = 0, i is nilpotent

• adj. equal to zero when raised to a certain power

## Etymologies

### from The American Heritage® Dictionary of the English Language, 4th Edition

nil + Latin potēns, potent-, having power; see potent.

## Examples

• There is nothing inconsistent with this restriction, and the positive L_m in isolation generate a gauge symmetry; there is no anomaly in the positive sector and thus a nilpotent BRST operator.

String Theory is Losing the Public Debate

• Hence this subalgebra admits a nilpotent BRST operator, and can be viewed as a gauge symmetry.

String Theory is Losing the Public Debate

• The BRST operator for the full Virasoro algebra is not nilpotent, and hence a global symmetry.

String Theory is Losing the Public Debate

• Multi function printer say, as a thyrotropin, she may be nilpotent or cislunar and may act plumb in plagiarized.

Rational Review

• One application of the solvable Freiman theorem is the following quantitative version of a classical result of Wolf, which asserts that any solvable group of polynomial growth is virtually nilpotent:

What's new

• x (for m ¥ 2) which George Boole had introduced in this form in his algebra of logic in 1847; and ˜nilpotent™, when xm = 0, for some m.

I Am Wearing Stolen Socks

• It provides a rigorous framework for mathematical analysis in which every function between spaces is smooth (i.e., differentiable arbitrarily many times, and so in particular continuous) and in which the use of limits in defining the basic notions of the calculus is replaced by nilpotent infinitesimals, that is, of quantities so small (but not actually zero) that some power ” most usefully, the square ” vanishes.

Continuity and Infinitesimals