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Interdisciplinary collaboration in pediatric palliative care: a qualitative study on barriers and facilitators as perceived by parents and healthcare professionals. [PDF]

Eur J Pediatr
Kemna MM, Aris-Meijer JL, Verhagen AAE, Teunissen SCCM, Engel M, Kars MC.   +5 more
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A Note on π-Engel Conditions

Southeast Asian Bulletin of Mathematics, 2001
For a set of primes \(\pi\), the concept of Engel conditions for finite groups is extended. For example an element \(g\) is a weakly right \(\pi\)-Engel element if for each \(\pi'\)-element \(x\) in the group \(G\) there is a positive integer \(n\) such that the \((n+1)\)-commutator \([x,g,\dots,g]\) is a \(\pi\)-element.
Fan, Yun, Hai, Jinke
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An Engel condition with skew derivations

Monatshefte für Mathematik, 2008
The authors extend [\textit{C. Lanski}, Proc. Am. Math. Soc. 118, No. 3, 731-734 (1993; Zbl 0821.16037)] from derivations to skew derivations. Let \(R\) be a prime ring and \(L\) a noncommutative Lie ideal of \(R\). For \(x,y\in R\) set \([x,y]_1=[x,y]=xy-yx\) and when \(n>1\) let \([x,y]_n=[[x,y]_{n-1},y]\).
Chou, Ming-Chu, Liu, Cheng-Kai
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Skew derivations with annihilating Engel conditions

Publicationes Mathematicae Debrecen, 2006
Let \(R\) be a noncommutative prime ring. Let \(\sigma\) be an automorphism of \(R\), \(\delta\) be a \(\sigma\)-derivation, and \(a\in R\). The authors prove that if \(a[\delta(x),x]_k=0\) for any \(x\in R\), where \(k\) is a fixed positive integer, then either \(a=0\) or \(\delta=0\), except when \(R=M_2(\text{GF}(2))\).
Chuang, C. L., Chou, M. C., Liu, C. K.
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RINGS SATISFYING GENERALIZED ENGEL CONDITIONS

Journal of Algebra and Its Applications, 2012
Let R be an associative ring and let x, y ∈ R. Define the generalized commutators as follows: [x, 0y] = x and [x, ky] = [x, k-1y]y - y[x, k-1y](k = 1, 2, …). In this paper we study some generalized Engel rings, i.e. [Formula: see text]-rings (satisfying [xm(x, y), k(x, y)y] = 0), [Formula: see text]-rings (satisfying [xm(x, y), k(x, y)yn(x, y)] = 0 ...
Ramezan-Nassab, M., Kiani, D.
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Engel Condition and p-nilpotency of Finite Groups

Acta Mathematica Sinica, English Series, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Lei, Qiu, Zheng Tian, Qiao, Shou Hong   +2 more
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Power closure and the Engel condition

Israel Journal of Mathematics, 1997
A Lie \(p\)-algebra \(L\) is called \(n\)-power closed if in every section of \(L\), any sum of two \(p^{i+n}\)-th powers is a \(p^i\)-th power \((i>0)\). The authors prove that if \(L\) is residually nilpotent and \(n\)-power closed for some \(n\geq 0\) then \(L\) is \((3p^{n+2}+1)\)-Engel if \(p\geq 2\) and \((3\cdot 2^{n+3}+1)\)-Engel if \(p=2 ...
Riley, David M., Semple, James F.
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On the Centralizers of Derivations with Engel Conditions

Communications in Algebra, 2013
Let R be a noncommutative prime ring and d, δ two nonzero derivations of R. If δ([d(x), x] n ) = 0 for all x ∈ R, then char R = 2, d 2 = 0, and δ = αd, where α is in the extended centroid of R. As an application, if char R ≠ 2, then the centralizer of the set {[d(x), x] n  | x ∈ R} in R coincides with the center of R.
Cheng-Kai Liu, Wen-Kwei Shiue
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On Certain Weak Engel-Type Conditions in Groups

Communications in Algebra, 2014
Let w(x, y) be a word in two variables and 𝔚 the variety determined by w. In this paper we raise the following question: if for every pair of elements a, b in a group G there exists g ∈ G such that w(a g , b) = 1, under what conditions does the group G belong to 𝔚? In particular, we consider the n-Engel word w(x, y) = [x, n y].
MERIANO, MAURIZIO, NICOTERA, Chiara
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