The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.
In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characteriz...In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of θ-part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation θto be transitive.展开更多
首先讨论GCN环的一些性质,其次证明了如下结果:1)设R为一个环,如果R上的二阶上三角矩阵环为GCN环,则R为约化环;2)GCN的exchange环R有稳定秩1;3)R为交换环当且仅当T={a 0 b c0 a 0 da,b,c,d,0 0 a e0 0 0ae∈R}是强GCN环;4)GCN的exchang...首先讨论GCN环的一些性质,其次证明了如下结果:1)设R为一个环,如果R上的二阶上三角矩阵环为GCN环,则R为约化环;2)GCN的exchange环R有稳定秩1;3)R为交换环当且仅当T={a 0 b c0 a 0 da,b,c,d,0 0 a e0 0 0ae∈R}是强GCN环;4)GCN的exchange环是左quasi-duo环.展开更多
Let R be a ring and n be a positive integer.Then R is called a left n-C2-ring(strongly left C2-ring)if every n-generated(finitely generated)proper right ideal of R has nonzero left annihilator.We discuss some n-C2 and...Let R be a ring and n be a positive integer.Then R is called a left n-C2-ring(strongly left C2-ring)if every n-generated(finitely generated)proper right ideal of R has nonzero left annihilator.We discuss some n-C2 and strongly C2 extensions,such as trivial extensions,formal triangular matrix rings,group rings and[D,C].展开更多
In this paper, we describe the structure of quadratic homogeneous polynomial maps F = X ＋ H with JH3 = 0. As a consequence we show that in dimension n ≤ 6, JH is strongly nilpotent, or equivalently F = X ＋ H is lin...In this paper, we describe the structure of quadratic homogeneous polynomial maps F = X ＋ H with JH3 = 0. As a consequence we show that in dimension n ≤ 6, JH is strongly nilpotent, or equivalently F = X ＋ H is linearly triangularizable.展开更多
A*-ring R is called a nil *-clean ring if every element of R is a sum of a projection and a nilpotent.Nil*-clean rings are the version of nil-clean rings introduced by Diesl.This paper is about the nil*-clean property...A*-ring R is called a nil *-clean ring if every element of R is a sum of a projection and a nilpotent.Nil*-clean rings are the version of nil-clean rings introduced by Diesl.This paper is about the nil*-clean property of rings with emphasis on matrix rings.We show that a*-ring R is nil*-clean if and only if J(R)is nil and R/J(R)is nil*-clean.For a 2-primal*-ring R,with the induced involution given by(aij)*=(a*ij)^(T),the nil*-clean property of Mn(R)is completely reduced to that of Mn(Zn).Consequently,Mn(R)is not a nil*-clean ring for n=3,4,and M2(R)is a nil*-clean ring if and only if J(R)is nil,R/J(R)is a Boolean ring and a*-a∈J(R)for all a∈R.展开更多
基金supported by NSFC (10871192)NSF of Hebei Province (A2010000194)
文摘The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.
文摘In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of θ-part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation θto be transitive.
文摘首先讨论GCN环的一些性质,其次证明了如下结果:1)设R为一个环,如果R上的二阶上三角矩阵环为GCN环,则R为约化环;2)GCN的exchange环R有稳定秩1;3)R为交换环当且仅当T={a 0 b c0 a 0 da,b,c,d,0 0 a e0 0 0ae∈R}是强GCN环;4)GCN的exchange环是左quasi-duo环.
文摘Let R be a ring and n be a positive integer.Then R is called a left n-C2-ring(strongly left C2-ring)if every n-generated(finitely generated)proper right ideal of R has nonzero left annihilator.We discuss some n-C2 and strongly C2 extensions,such as trivial extensions,formal triangular matrix rings,group rings and[D,C].
文摘In this paper, we describe the structure of quadratic homogeneous polynomial maps F = X ＋ H with JH3 = 0. As a consequence we show that in dimension n ≤ 6, JH is strongly nilpotent, or equivalently F = X ＋ H is linearly triangularizable.
基金This research was supported by Anhui Provincial Natural Science Foundation(No.2008085MA06)the Key Project of Anhui Education Committee(No.gxyqZD2019009)(for Cui)a Discovery Grant from NSERC of Canada(for Xia and Zhou).
文摘A*-ring R is called a nil *-clean ring if every element of R is a sum of a projection and a nilpotent.Nil*-clean rings are the version of nil-clean rings introduced by Diesl.This paper is about the nil*-clean property of rings with emphasis on matrix rings.We show that a*-ring R is nil*-clean if and only if J(R)is nil and R/J(R)is nil*-clean.For a 2-primal*-ring R,with the induced involution given by(aij)*=(a*ij)^(T),the nil*-clean property of Mn(R)is completely reduced to that of Mn(Zn).Consequently,Mn(R)is not a nil*-clean ring for n=3,4,and M2(R)is a nil*-clean ring if and only if J(R)is nil,R/J(R)is a Boolean ring and a*-a∈J(R)for all a∈R.
