On when an element of the coefficient ring of a ring spectrum is nilpotent
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 complex cobordism spectrum . More precisely, it states that for any ring spectrum , the kernel of the map consists of nilpotent elements.[1] It was conjectured by Douglas Ravenel (1984) and proved by Ethan S. Devinatz, Michael J. Hopkins, and Jeffrey H. Smith (1988).
^Lurie, Jacob (April 27, 2010). "The Nilpotence Theorem (Lecture 25)" (PDF). Archived (PDF) from the original on January 30, 2022.
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In algebraic topology, the nilpotencetheorem gives a condition for an element in the homotopy groups of a ring spectrum to be nilpotent, in terms of the...
^{\infty }} of C P ∞ {\displaystyle \mathbb {CP} ^{\infty }} . The nilpotencetheorem states that, for any ring spectrum R {\displaystyle R} , the kernel...
{\displaystyle {\mathfrak {N}}} ; this is a consequence of the binomial theorem. This ideal is the nilradical of the ring. Every nilpotent element x {\displaystyle...
sequence Chromatic homotopy theory Equivariant stable homotopy theory Nilpotencetheorem Serre, Jean-Pierre (1953). "Groupes d'homotopie et classes de groupes...
element of non-zero degree is nilpotent; the nilpotencetheorem on complex cobordism implies Nishida's theorem.[citation needed] Example: If η is the generator...
*-algebras. p. 1283. For the term, compare Engel's theorem, also on nilpotency. Bechtell (1971), p. 51, Theorem 5.1.3 Isaacs (2008), Thm. 1.26 Bechtell, Homer...
Jordan normal form, up to a permutation of the Jordan blocks Index of nilpotence Elementary divisors, which form a complete set of invariants for similarity...
France, ISBN 978-2-85629-164-1, MR 2115000 Voevodsky, V. (1995), "A nilpotencetheorem for cycles algebraically equivalent to 0", Int. Math. Res. Notices...
p-nilpotence and various non-simplicity criteria focussing on showing that a finite group has a normal subgroup of index p. The focal subgroup theorem relates...
work on Thom spectra. This work was used heavily in the proof of the nilpotencetheorem by Ethan Devinatz, Michael J. Hopkins, and Jeffrey Smith. In 1998...
Notes 117, Cambridge Univ. Press, Cambridge, 1987 V. Voevodsky, A nilpotencetheorem for cycles algebraically equivalent to zero. Internat. Math. Res....
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...
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...
matrix defined as Nij = δi,j−1 (where δ is the Kronecker delta). The nilpotency of N can be exploited when calculating f(A) where f is a complex analytic...
group. Frobenius groups whose Fitting subgroup has arbitrarily large nilpotency class were constructed by Ito: Let q be a prime power, d a positive integer...
exclusively with finite groups. The nilpotency of the Fitting subgroup of a finite group is guaranteed by Fitting's theorem which says that the product of...
we will not prove here. A somewhat easier equivalent condition for the nilpotency of g {\displaystyle {\mathfrak {g}}} : g {\displaystyle {\mathfrak {g}}}...
, {\displaystyle V=\bigoplus _{n>0}V^{n},} satisfying the following "nilpotence condition" on its differential d: the space V is the union of an increasing...
Witten genus and the theorem of the cube. Invent. Math. 146 (2001), no. 3, 595–687. (with Matthew Ando and Neil Strickland) Nilpotence and stable homotopy...
Soc. p. 332. ISBN 978-0-8218-4640-7. McCrimmon, Kevin (1983). "Strong nilpotence of solvable ideals in quadratic Jordan algebras" (PDF). Journal of Algebra...
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