Results 91 to 100 of about 1,062 (223)
A note on rings with central nilpotent elements [PDF]
Proceedings of the American Mathematical Society, 1954 PROOF. Since xn+lp(X)=Xn, we have that (x2p(x)-x)xn-'=O (we can assume that n > 1 for this could always be achieved by multiplying both sides of the equation by x). Now, each term of (x2p(x) -x)ninvolves x to a power which is at least n-1; therefore (x2p(x) -x)n = (x2p(x) -x) (x2p(x) -x)n= 0.
openaire +1 more source
Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré +4 more
wiley +1 more source
Nilpotent elements in the Green ring
Journal of Algebra, 1986 Let k be a field of characteristic p and G a finite group. Theorem 2.1 is a generalization of a theorem of Landrock for the absolutely irreducible case: Suppose that M and N are absolutely indecomposable kG-modules. Then \(M\otimes N\) has the trivial module k as a direct summand if and only if the following two conditions are satisfied: (i) \(M\cong N^
Benson, D.J, Carlson, J.F
openaire +1 more source
The Global Glimm Property for C*‐algebras of topological dimension zero
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract We show that a C∗$C^*$‐algebra with topological dimension zero has the Global Glimm Property (every hereditary subalgebra contains an almost full nilpotent element) if and only if it is nowhere scattered (no hereditary subalgebra admits a finite‐dimensional representation). This solves the Global Glimm Problem in this setting.
Ping Wong Ng +2 more
wiley +1 more source
, 2010 Let g be a simple complex Lie algebra and let e be a nilpotent element of g. It was conjectured by Premet in [P07i] that the finite W-algebra U(g; e) admits a 1-dimensional representation, and further work [L10, P08] has reduced this conjecture to the ...
Ubly, Glenn
core
Central Subalgebras Of The Centralizer Of A Nilpotent Element
Let G be a connected, semisimple algebraic group over a field k whose characteristic is very good for G. In a canonical manner, one associates to a nilpotent element X is an element of Lie(G) a parabolic subgroup P - in characteristic zero, P may be ...
Mcninch, George J., Testerman, Donna M.
core +1 more source
Locally nilpotent derivations of free algebra of rank two [PDF]
, 2019 In commutative algebra, if $\delta$ is a locally nilpotent derivation of the polynomial algebra $K[x_1,\ldots,x_d]$ over a field $K$ of characteristic 0 and $w$ is a nonzero element of the kernel of $\delta$, then $\Delta=w\delta$ is also a locally ...
Drensky, V., Makar-Limanov, L.
core +1 more source
A classification of Prüfer domains of integer‐valued polynomials on algebras
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract Let D$D$ be an integrally closed domain with quotient field K$K$ and A$A$ a torsion‐free D$D$‐algebra that is finitely generated as a D$D$‐module and such that A∩K=D$A\cap K=D$. We give a complete classification of those D$D$ and A$A$ for which the ring IntK(A)={f∈K[X]∣f(A)⊆A}$\textnormal {Int}_K(A)=\lbrace f\in K[X] \mid f(A)\subseteq A ...
Giulio Peruginelli, Nicholas J. Werner
wiley +1 more source
Zero divisors and nilpotent elements in power series rings
, 1971 It is well known that a polynomial f ( X ) f(X) over a commutative ring R R with identity is nilpotent if and only if each coefficient of f ( X )
David E. Fields
core +1 more source
Hyperkähler metrics on the regular nilpotent adjoint orbit
, 2020 This thesis studies the Kronheimer hyperkähler metric on the adjoint orbit of the classical Lie group SL_n (C) of a regular, nilpotent element in its Lie algebra sl_n(C).
Sonderegger, Oliver
core +1 more source