We define perfect ideals,near perfect ideals and upper bounded ideals of a finite-dimensional Lie superalgebra,and study the properties of these three kinds of ideals through their relevant sequences.We prove that a L...We define perfect ideals,near perfect ideals and upper bounded ideals of a finite-dimensional Lie superalgebra,and study the properties of these three kinds of ideals through their relevant sequences.We prove that a Lie superalgebra is solvable if and only if its maximal perfect ideal is zero,or its quotient superalgebra by the maximal perfect ideal is solvable.We also show that a Lie superalgebra is nilpotent if and only if its maximal near perfect ideal is zero.Moreover,we prove that a nilpotent Lie superalgebra has only one upper bounded ideal,which is the nilpotent Lie superalgebra itself.展开更多
For an ideal I of a Noetherian local ring （R, m, k） one hasβR1（I） -β0R（I） ≥-1. It is demonstrated that some residual intersections of an ideal I for whichβ1R（I） -β0R（I） = -1 or 0 are perfect.
基金Supported by NNSF of China(Nos.11771069 and 12071405).
文摘We define perfect ideals,near perfect ideals and upper bounded ideals of a finite-dimensional Lie superalgebra,and study the properties of these three kinds of ideals through their relevant sequences.We prove that a Lie superalgebra is solvable if and only if its maximal perfect ideal is zero,or its quotient superalgebra by the maximal perfect ideal is solvable.We also show that a Lie superalgebra is nilpotent if and only if its maximal near perfect ideal is zero.Moreover,we prove that a nilpotent Lie superalgebra has only one upper bounded ideal,which is the nilpotent Lie superalgebra itself.
文摘For an ideal I of a Noetherian local ring （R, m, k） one hasβR1（I） -β0R（I） ≥-1. It is demonstrated that some residual intersections of an ideal I for whichβ1R（I） -β0R（I） = -1 or 0 are perfect.
