In this paper,we study the notion of McCoy ring over the class of non-commutative rings of polynomial type known as skew Poincare–Birkhoff–Witt extensions.As a consequence,we generalize several results about this no...In this paper,we study the notion of McCoy ring over the class of non-commutative rings of polynomial type known as skew Poincare–Birkhoff–Witt extensions.As a consequence,we generalize several results about this notion considered in the literature for commutative rings and Ore extensions.展开更多
The aim of this paper is to investigate different radicals(Wedderburn radical,lower nil radical,Levitzky radical,upper nil radical,the set of all nilpotent elements,the sum of all nil left ideals)of the noncommutative...The aim of this paper is to investigate different radicals(Wedderburn radical,lower nil radical,Levitzky radical,upper nil radical,the set of all nilpotent elements,the sum of all nil left ideals)of the noncommutative rings known as skew Poincare–Birkhoff–Witt extensions.We characterize minimal prime ideals of these rings and prove that the Kothe’s conjecture holds for these extensions.Finally,we establish the transfer of several ring-theoretical properties(reduced,symmetric,reversible,2-primal)from the coefficients ring of a skew PBW extension to the extension itself.展开更多
基金Research is supported by Grant HERMES CODE 30366Departamento de Matemati-cas,Facultad de Ciencias,Universidad Nacional de Colombia,Sede Bogota.
文摘In this paper,we study the notion of McCoy ring over the class of non-commutative rings of polynomial type known as skew Poincare–Birkhoff–Witt extensions.As a consequence,we generalize several results about this notion considered in the literature for commutative rings and Ore extensions.
基金The first author was supported by the research fund of Facultad de Ciencias,Code HERMES 41535,Universidad Nacional de Colombia,Bogota,Colombia。
文摘The aim of this paper is to investigate different radicals(Wedderburn radical,lower nil radical,Levitzky radical,upper nil radical,the set of all nilpotent elements,the sum of all nil left ideals)of the noncommutative rings known as skew Poincare–Birkhoff–Witt extensions.We characterize minimal prime ideals of these rings and prove that the Kothe’s conjecture holds for these extensions.Finally,we establish the transfer of several ring-theoretical properties(reduced,symmetric,reversible,2-primal)from the coefficients ring of a skew PBW extension to the extension itself.
