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Agata Smoktunowicz - One of the best experts on this subject based on the ideXlab platform.
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differential polynomial rings over locally nilpotent rings need not be Jacobson Radical
Journal of Algebra, 2014Co-Authors: Agata Smoktunowicz, Michal ZiembowskiAbstract:Abstract We answer a question by Shestakov on the Jacobson Radical in differential polynomial rings. We show that if R is a locally nilpotent ring with a derivation D then R [ X ; D ] need not be Jacobson Radical. We also show that J ( R [ X ; D ] ) ∩ R is a nil ideal of R in the case where D is a locally nilpotent derivation and R is an algebra over an uncountable field.
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differential poynomial rings over locally nilpotent rings need not be Jacobson Radical
arXiv: Rings and Algebras, 2013Co-Authors: Agata Smoktunowicz, Michal ZiembowskiAbstract:We answer a question by Shestakov on the Jacobson Radical in differential polynomial rings. We show that if R is a locally nilpotent ring with a derivation D then R[X;D] need not be Jacobson Radical. We also show that J(R[X;D])\cap R is a nil ideal of R in the case where D is a locally nilpotent derivation and R is an algebra over an uncountable field.
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Jacobson Radical algebras with quadratic growth
Glasgow Mathematical Journal, 2013Co-Authors: Agata Smoktunowicz, Alexander YoungAbstract:In this paper, it is shown that over every countable algebraically closed field K there exists a finitely generated K-algebra that is Jacobson Radical, infinite dimensional, generated by two elements, graded, and has quadratic growth. We also propose a way of constructing examples of algebras with quadratic growth that satisfy special types of relations. 2010 Mathematics subject classification: 16N40, 16P90
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Jacobson Radical non nil algebras of gel fand kirillov dimension 2
Israel Journal of Mathematics, 2013Co-Authors: Agata Smoktunowicz, Laurent BartholdiAbstract:For an arbitrary countable field, we construct an associative algebra that is graded, generated by finitely many degree-1 elements, is Jacobson Radical, is not nil, is prime, is not PI, and has Gel’fand-Kirillov dimension two. This refutes a conjecture incorrectly attributed to Goodearl.
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on a conjecture of goodearl Jacobson Radical non nil algebras of gelfand kirillov dimension 2
arXiv: Rings and Algebras, 2013Co-Authors: Agata Smoktunowicz, Laurent BartholdiAbstract:For an arbitrary countable field, we construct an associative alge- bra that is graded, generated by finitely many degree-1 elements, is Jacobson Radical, is not nil, is prime, is not PI, and has Gelfand-Kirillov dimension two. This refutes a conjecture attributed to Goodearl.
Antonios Manoussos - One of the best experts on this subject based on the ideXlab platform.
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the Jacobson Radical for analytic crossed products
Journal of Functional Analysis, 2001Co-Authors: Allan P Donsig, A Katavolos, Antonios ManoussosAbstract:We characterise the Jacobson Radical of an analytic crossed product C0(X)×φ Z+, answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Jacobson Radical of analytic crossed products C0(X)×φ Zd+. This consists of all elements whose “Fourier coefficients” vanish on the recurrent points of the dynamical system (and the first one is zero). The multidimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.
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the Jacobson Radical for analytic crossed products
arXiv: Operator Algebras, 2000Co-Authors: Allan P Donsig, A Katavolos, Antonios ManoussosAbstract:We characterise the (Jacobson) Radical of the analytic crossed product of C_0(X) by the non-negative integers (Z_+), answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Radical of analytic crossed products of C_0(X) by (Z_+)^d. The Radical consists of all elements whose `Fourier coefficients' vanish on the recurrent points of the dynamical system (and the first one is zero). The multi-dimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.
Justin R Peters - One of the best experts on this subject based on the ideXlab platform.
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semicrossed products of the disk algebra and the Jacobson Radical
Canadian Mathematical Bulletin, 2014Co-Authors: Anchalee Khemphet, Justin R PetersAbstract:We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products. We characterize the Jacobson Radical of these operator algebras. Furthermore, in the case the finite Blaschke product is elliptic, we show that the semicrossed product contains no nonzero quasinilpotent elements. However, if the finite Blaschke product is hyperbolic or parabolic with zero hyperbolic step, the Jacobson Radical is nonzero and a proper subset of the set of quasinilpotent elements.
Anchalee Khemphet - One of the best experts on this subject based on the ideXlab platform.
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semicrossed products of the disk algebra and the Jacobson Radical
Canadian Mathematical Bulletin, 2014Co-Authors: Anchalee Khemphet, Justin R PetersAbstract:We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products. We characterize the Jacobson Radical of these operator algebras. Furthermore, in the case the finite Blaschke product is elliptic, we show that the semicrossed product contains no nonzero quasinilpotent elements. However, if the finite Blaschke product is hyperbolic or parabolic with zero hyperbolic step, the Jacobson Radical is nonzero and a proper subset of the set of quasinilpotent elements.
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the Jacobson Radical of semicrossed products of the disk algebra
2012Co-Authors: Anchalee KhemphetAbstract:In this thesis, we characterize the Jacobson Radical of the semicrossed product A(D)×α Z+ of the disk algebra by an endomorphism α where α is defined by the composition with a finite Blaschke product φ. Precisely, the Jacobson Radical is the set of those whose 0th Fourier coefficient is identically zero and whose kth Fourier coefficient vanishes on the set of recurrent points of φ. Moreover, if φ is elliptic, i.e., φ has a fixed point in the open unit disc, then the Jacobson Radical coincides with the set of quasinilpotent elements.
Allan P Donsig - One of the best experts on this subject based on the ideXlab platform.
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the Jacobson Radical for analytic crossed products
Journal of Functional Analysis, 2001Co-Authors: Allan P Donsig, A Katavolos, Antonios ManoussosAbstract:We characterise the Jacobson Radical of an analytic crossed product C0(X)×φ Z+, answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Jacobson Radical of analytic crossed products C0(X)×φ Zd+. This consists of all elements whose “Fourier coefficients” vanish on the recurrent points of the dynamical system (and the first one is zero). The multidimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.
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the Jacobson Radical for analytic crossed products
arXiv: Operator Algebras, 2000Co-Authors: Allan P Donsig, A Katavolos, Antonios ManoussosAbstract:We characterise the (Jacobson) Radical of the analytic crossed product of C_0(X) by the non-negative integers (Z_+), answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Radical of analytic crossed products of C_0(X) by (Z_+)^d. The Radical consists of all elements whose `Fourier coefficients' vanish on the recurrent points of the dynamical system (and the first one is zero). The multi-dimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.