Commutators - Open Access .click

1964
The aim of this section is to show, by means of the methods developed in Chapter 3, that for an associative H-space G there exist maps G× G → G satisfying certain commutativity conditions (Theorem 4.5). As will be explained in Remarks 4.6 this result is related to the work of other authors on homotopy-commutativity.
M. Arkowitz, C. R. Curjel
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On Commutativity and Strong Commutativity-Preserving Maps

Canadian Mathematical Bulletin, 1994
AbstractIf R is a ring and S ⊆ R, a mapping f:R —> R is called strong commutativity- preserving (scp) on S if [x, y] = [f(x),f(y)] for all x,y € S. We investigate commutativity in prime and semiprime rings admitting a derivation or an endomorphism which is scp on a nonzero right ideal.
Bell, Howard E., Daif, Mohamad Nagy
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On Non-Commutative Algebras and Commutativity Conditions

Results in Mathematics, 1990
A theorem of T. Nakayama states that an algebra \(A\) over an \({\mathcal N}\)- ring \(R\) is commutative if \(A\) satisfies the following condition: (N) For each \(x\) in \(A\), there exists \(f(X)\) in \(X^ 2 R[X]\) such that \(x-f(x)\) is central. More generally, W. Streb studied \(R\)-algebras \(A\) satisfying the following condition: (S) For each \
Komatsu, Hiroaki, Tominaga, Hisao
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commutator
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mathematics
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commutativity
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commutativity theorems