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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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Commutativity of rings with constraints on commutators
Results in Mathematics, 1985Let F denote a commutative ring, \(F\) the corresponding ring of polynomials in two non-commuting indeterminates, and F[X,Y] the ring of polynomials in two commuting indeterminates. A polynomial \(f(X,Y)\in F\) is called admissible if each of its monomials has length at least 3 and f(X,Y) has trivial image under the natural F-algebra map from \(F\) to ...
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The Mathematical Gazette, 1947
We prove some theorems on commutative involutions in a “real” projective geometry in which cobasal homographie ranges may have 0, 1 or 2 self-corresponding points (and therefore a conic and a general line in its plane have 0, 1 or 2 points of intersection).
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We prove some theorems on commutative involutions in a “real” projective geometry in which cobasal homographie ranges may have 0, 1 or 2 self-corresponding points (and therefore a conic and a general line in its plane have 0, 1 or 2 points of intersection).
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Commutativity of rings with constraints on commutators
2000This paper studies commutativity of rings \(R\) satisfying polynomial identities of the form\break \(x^t[x^n,y]y^r=[x,y^m]y^s\) and three similar forms, where \(n,m,r,s,t\) are suitably-chosen nonnegative integers. Whether the theorems are correct as stated is not clear, but for some \((n,m,r,s,t)\) the proofs given do not work.
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