Results 151 to 160 of about 1,081 (183)

The nilpotence degree of quantum Lie nilpotent algebras

International Journal of Algebra and Computation, 2018
We consider the quantum analog of the Lie commutator [Formula: see text] for an invertible element [Formula: see text] of the ground field and prove lower and upper bounds for the nilpotence degree of an associative algebra satisfying an identity of the form [Formula: see text].
Elena Kireeva, Vladimir Shchigolev
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RINGS OVER WHICH COEFFICIENTS OF NILPOTENT POLYNOMIALS ARE NILPOTENT

International Journal of Algebra and Computation, 2011
Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, observing the structure of nilpotent elements in Armendariz rings and introducing the notion of nil-Armendariz rings. The class of nil-Armendariz rings contains Armendariz rings and NI rings.
Tai Keun Kwak, Yang Lee
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On the n—nilpotency

Results in Mathematics, 2002
The main question discussed in the paper under review is some cases of the following: Does an algebra (not necessarily associative) have a property \(\mathcal P\) if it is the sum of two ideals each of which has the property \(\mathcal P\)? If a group is the product of two normal subgroups having a property \(\mathcal P\), does it have itself the ...
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NILPOTENCY IN UNCOUNTABLE GROUPS

Journal of the Australian Mathematical Society, 2016
The main purpose of this paper is to investigate the behaviour of uncountable groups of cardinality $\aleph$ in which all proper subgroups of cardinality $\aleph$ are nilpotent. It is proved that such a group $G$ is nilpotent, provided that $G$ has no infinite simple homomorphic images and either $\aleph$ has cofinality strictly larger than $\aleph _{0}
De Giovanni, Francesco, Trombetti, Marco
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A (locally nilpotent)-by-nilpotent variety of groups

Mathematical Proceedings of the Cambridge Philosophical Society, 2002
Given positive integers k and n, let [Xfr ] be the class of all groups G such that γk(G) is locally nilpotent and [x1, x2, …, xk]n = 1 for any x1, x2, …, xk ∈ G. It is shown that [Xfr ] is a variety.
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Minimal Non-nilpotent and Locally Nilpotent Fusion Systems

Algebra Colloquium, 2016
The main purpose of this note is to show that there is a one-to-one correspondence between minimal non-nilpotent (resp., locally nilpotent) saturated fusion systems and finite p′-core-free p-constrained minimal non-nilpotent (resp., locally p-nilpotent) groups.
Liao, Jun, Liu, Yanjun
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A note on a nilpotent lower bound of nilpotent triangular norms

Fuzzy Sets and Systems, 1999
The authors prove that there exists a nilpotent upper (! see corrigendum) bound for a finite set of nilpotent t-norms. Essential tools for the proof are additive generators of t-norms and the theory of superadditive functions. An illustrative example is presented.
Vladimír Marko, Radko Mesiar
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Nilpotent SQS-skeins with nilpotent derived sloops

Ars Comb., 2000
SQS-skeins are an algebraic description of \(3\)-\((v,4,1)\) designs (i.e., Steiner quadruple systems). Each such design determines a ternary operation, say \(q\), that gives a missing element of a block, whenever the arguments are pairwise distinct. If some arguments coincide, then the result is determined so that \(q\) becomes a Mal'tsev operation ...
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Nilpotent Numbers

The American Mathematical Monthly, 2000
Jonathan Pakianathan, Krishnan Shankar
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Homotopy nilpotency and co-nilpotency of spaces

2020
We review known and state some new results on homotopy nilpotency and co-nilpotency of spaces. Next, we take up the systematic study of homotopy nilpotency of homogenous spaces G/K for a Lie group G and its closed subgroup K < G. Then, the homotopy nilpotency of the loop spaces Ω(Gn,m(K)) and Ω(Vn,m(K)) of Grassmann Gn,m(K) and Stiefel Vn,m(K ...
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