Definition of Nilpotence. Meaning of Nilpotence. Synonyms of Nilpotence

- In mathematics, an element x {\displaystyle x} of a ring R {\displaystyle R} is called nilpotent if there exists some positive integer n {\displaystyle...
- In algebraic topology, the nilpotence theorem gives a condition for an element in the homotopy groups of a ring spectrum to be nilpotent, in terms of the...
- Both of these concepts are special cases of a more general concept of nilpotence that applies to elements of rings. The matrix A = [ 0 1 0 0 ] {\displaystyle...
- forms of the definition of nilpotency, that the trivial group is the unique group of nilpotency class 0, and groups of nilpotency class 1 are exactly the...
- first of the seven conjectures, then the nilpotence conjecture, was proved in 1988 and is now known as the nilpotence theorem. The telescope conjecture, which...
- particularly important, since it is an example of a 2-group of maximal nilpotency class. In Bertram Huppert's text Endliche Gruppen, this group is called...
- an anticommutative algebra) and has the further property that x2 = 0 (nilpotence) for every homogeneous element x of odd degree. The differential forms...
- in the stable homotopy category than you might think. For example, the nilpotence conjecture states that some suspension of some iteration of a map between...
- (x_{n})=\pi (x)_{n}} . The Jordan decomposition can be used to characterize nilpotency of an endomorphism. Let k be an algebraically closed field of characteristic...
- of Mathematics on "nilpotence and stable homotopy". Devinatz, Ethan S.; Hopkins, Michael J.; Smith, Jeffrey H. (1988). "Nilpotence and stable homotopy...