Results 221 to 230 of about 4,370 (257)
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On Commutativity and Strong Commutativity-Preserving Maps
Canadian Mathematical Bulletin, 1994AbstractIf 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, 1990A 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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Commutators and the Commutator Subgroup
The American Mathematical Monthly, 1977(1977). Commutators and the Commutator Subgroup. The American Mathematical Monthly: Vol. 84, No. 9, pp. 720-722.
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On Abelian Groups with Commutative Commutators of Endomorphisms
Journal of Mathematical Sciences, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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36th International Symposium on Multiple-Valued Logic (ISMVL'06), 2006
Centralizer of a set of hyperoperations F is a clone of hyperoperations that commute with all hyperoperations from F. There are several ways to define this commuting operator which imply several definitions of centralizers of sets of hyperoperations and they are considered in this paper. In order to obtain their properties, we discuss the definition of
Jovanka Pantovic, Gradimir Vojvodic
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Centralizer of a set of hyperoperations F is a clone of hyperoperations that commute with all hyperoperations from F. There are several ways to define this commuting operator which imply several definitions of centralizers of sets of hyperoperations and they are considered in this paper. In order to obtain their properties, we discuss the definition of
Jovanka Pantovic, Gradimir Vojvodic
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International Journal of Algebra and Computation
In this paper, we investigate properties of varieties of algebras described by a novel concept of equation that we call commutator equation. A commutator equation is a relaxation of the standard term equality obtained substituting the equality relation with the commutator relation.
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In this paper, we investigate properties of varieties of algebras described by a novel concept of equation that we call commutator equation. A commutator equation is a relaxation of the standard term equality obtained substituting the equality relation with the commutator relation.
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Commute Replacement and Commute Displacement
Transportation Research Record: Journal of the Transportation Research Board, 2008Working by telecommunication has been the subject of research attention in transportation studies for many years. Particular consideration has been given to occasional working from home (home working) by (full-time, paid) employees who represent a tangible removal of commute trips on days that people work from home.
Glenn Lyons, Hebba Haddad
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Commutativity of Rings with Constraints on Commutators, II
Results in Mathematics, 2000[For part I see ibid. 5, 123-131 (1985; Zbl 0606.16023).] The author proves commutativity of an associative ring \(R\) satisfying one of the following conditions: (1) for each \(x,y\in R\) there exists a co-monic polynomial \(p(t)\in tZ[t]\), such that \([x,y]=[x,y](p(xy)-p(yx))\); (2) for each \(x,y\in R\) there exist \(p(t),q(t)\in tZ[t]\) with \(q(t)
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Commutativity of rings with powers commuting on subsets
Mathematical Journal of Okayama University, 1997Let \(R\) denote a ring with 1; let \(w=w(X,Y)\) denote a word, possibly 1, in two noncommuting indeterminates; and let \(n\) be a positive integer. The elements \(x,y\in R\) are said to satisfy condition \(a(w,n)\) (resp. \(b(w,n)\)) if \(w(x,y)[x^n,y^n]=0\) (resp. \(w(x,y)((xy)^n-(yx)^n)=0\)). Define \(A\subseteq R\) to be a \(P\)-subset if for each \
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On the Commutativity of Rings with Constraints on Commutators.
International Journal of Mathematics and Computer ScienceWe investigate the commutativity of rings with identity satisfying identities involving commutators and their powers in the class of M!-torsion-free rings. We obtain sufficient conditions for commutativity from identities of the forms [x,y^m]=0, [x^n,y^m]=0, and [x^n,y]=[x,y^m], as well as from conditions on mappings preserving commutators.
Utsanee Leerawat, Chitlada Somsup
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