Results 21 to 30 of about 3,997 (207)
On central commutator Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, 2000 Let B be a ring with 1, G a finite automorphism group of B of order n for some integer n, BG the set of elements in B fixed under each element in G, and Δ=VB(BG) the commutator subring of BG in B.
George Szeto, Lianyong Xue
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MATHEMATICA SCANDINAVICA, 1988 Let \({\mathcal B}\) be a Banach space, \(\sigma\) a \(C_ 0\)-group of isometries of \({\mathcal B}\) with generator \(H\), and \({\mathcal D}\subseteq D(H)\) a \(\sigma\)-invariant core of \(H\). Suppose \(K:{\mathcal D}\to {\mathcal B}\) is a dissipative operator satisfying \[ 1.\quad \| Ka\| \leq k_ 0(\| Ha\| \vee \| a\|),\quad a\in {\mathcal D}, \]
Batty, Charles J.K., Robinson, Derek W.
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Commutators and commutator subgroups of finite p-groups [PDF]
Journal of Algebra, 2021 28 pages.
Rahul Kaushik, Manoj K. Yadav
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Groups with minimax commutator subgroup [PDF]
International Journal of Group Theory, 2014 A result of Dixon, Evans and Smith shows that if $G$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian, then $G$ itself has this property, i.e. the commutator subgroup of~$G$ has finite rank.
Francesco de Giovanni, Trombetti
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A Pair of Derivations on Prime Rings with Antiautomorphism
Mathematics, 2023 This article examines the commutativity of rings with antiautomorphisms, specifically when they are equipped with derivations that satisfy certain algebraic identities.
Faez A. Alqarni +4 more
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A note on rings with certain variables identities
International Journal of Mathematics and Mathematical Sciences, 1989 It is proved that certain rings satisfying generalized-commutator constraints of the form [xm,yn,yn,...,yn]=0 with m and n depending on x and y, must have nil commutator ideal.
Hazar Abu-Khuzam
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COMMUTATIVITY THEOREMS FOR RINGS WITH CONSTRAINTS ON COMMUTATORS
Tamkang Journal of Mathematics, 1995 Let $R$ be a left (resp. right) $s$-unital ring and $m$ be a positive integer. Suppose that for each $y$ in $R$ there exist $J(t)$, $g(t)$, $h(t)$ in $Z[t]$ such that $x^m[x,y]= g(y)[x,y^2f(y)]h(y)$ (resp. $[x,y]x^m= g(y)[x,y^2f(y)]h(y))$ for all $x$ in $R$. Then $R$ is commutative (and conversely).
Abujabal, H. A. S., Ashraf, Mohd.
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Generating Sets and a Structure of the Wreath Product of Groups with Non-Faithful Group Action
International Journal of Analysis and Applications, 2020 Given a permutational wreath product sequence of cyclic groups, we investigate its minimal generating set, the minimal generating set for its commutator and some properties of its commutator subgroup.
Ruslan Skuratovskii
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Stone and Flat Topologies on the Minimal Prime Spectrum of a Commutator Lattice
AxiomsIn previous work we have studied minimal prime spectra, as well as extensions of universal algebras whose term condition commutator behaves like the modular commutator in the sense that it is commutative and distributive with respect to arbitrary joins ...
George Georgescu +2 more
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Commutators and Squares in Free Nilpotent Groups
International Journal of Mathematics and Mathematical Sciences, 2009 In a free group no nontrivial commutator is a square. And in the free group F2=F(x1,x2) freely generated by x1,x2 the commutator [x1,x2] is never the product of two squares in F2, although it is always the product of three squares.
Mehri Akhavan-Malayeri
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