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Noncommutative oscillators are first-quantized through an abelian Drinfel’d twist deformation of a Hopf algebra and its action on a module. Several impor-tant and subtle issues making possible the qua...
In this paper, we mainly study the derivation algebra of the free Lie algebra and the Chen Lie algebra generated by the abelianization H of a free group, and trace maps.
We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite derivation subalgebra such that the commutative associati...
In this paper, the k-derivation is defined on a G-ring M (that is, if M is a G-ring, d:M\to M and k:G\to G are to additive maps such that d(ab b )= d(a)b b + ak(b)b + ab d(b) for all a,b\in M, \quad b...
A precise formulation for the relations among certain variables under a set of polynomial equations and a set of polynomial inequations (to exclude certain special cases which cannot be excluded by th...

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