Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using t...Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.展开更多
We consider the sufficient and necessary conditions for the formal triangular matrix ring being right minsymmetric, right DS, semicommutative, respectively.
An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of...An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.展开更多
In this paper we study the formal triangular matrix ring T =and give some necessary and sufficient conditions for T to be (strongly) separative, m-fold stable and unit 1-stable. Moreover, a condition for finitely gene...In this paper we study the formal triangular matrix ring T =and give some necessary and sufficient conditions for T to be (strongly) separative, m-fold stable and unit 1-stable. Moreover, a condition for finitely generated projec-tive T-modules to have n in the stable range is given under the assumption that A and B are exchange rings.展开更多
In this paper the sufficient and necessary conditions are given for a formal triangular matrix ring to be right PP, generalized right PP, or semihereditary, respectively.
A ring R is said to be right McCoy if the equation f（x）g（x） = 0, where y（x） and g（x） are nonzero polynomials of R[x], implies that there exists nonzero s E R such that f（x）s = 0. It is proven that no proper ...A ring R is said to be right McCoy if the equation f（x）g（x） = 0, where y（x） and g（x） are nonzero polynomials of R[x], implies that there exists nonzero s E R such that f（x）s = 0. It is proven that no proper （triangular） matrix ring is one-sided McCoy. It is shown that for many polynomial extensions, a ring R is right Mccoy if and only if the polynomial extension over R is right Mccoy.展开更多
The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- reg...The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.展开更多
设T=A 0 U B是形式三角矩阵环,其中A,B是环,U是(B,A)-双模.利用Hom函子和伴随同构等理论,刻画形式三角矩阵环T上的F-Gorenstein平坦模结构,并证明若BU的平坦维数有限,U A的平坦维数有限且对任意的余挠左A-模C,有U■AC是余挠左B-模,则左T...设T=A 0 U B是形式三角矩阵环,其中A,B是环,U是(B,A)-双模.利用Hom函子和伴随同构等理论,刻画形式三角矩阵环T上的F-Gorenstein平坦模结构,并证明若BU的平坦维数有限,U A的平坦维数有限且对任意的余挠左A-模C,有U■AC是余挠左B-模,则左T-模M_(1)/M_(2)φ^(M)是F-Gorenstein平坦模当且仅当M_(1)是F-Gorenstein平坦左A-模,Cokerφ^(M)是F-Gorenstein平坦左B-模,且φ^(M):U■AM 1→M_(2)是单射.展开更多
引入拟正则Armendariz环并研究其性质。证明弱Armendariz环是拟正则Armendariz环,直积∏i∈I R i是拟正则Armendariz环当且仅当每个环R i(i∈I)是拟正则Armendariz环,同时证明R是拟正则Armendariz环当且仅当上三角矩阵环T n(R)(n≥2)是...引入拟正则Armendariz环并研究其性质。证明弱Armendariz环是拟正则Armendariz环,直积∏i∈I R i是拟正则Armendariz环当且仅当每个环R i(i∈I)是拟正则Armendariz环,同时证明R是拟正则Armendariz环当且仅当上三角矩阵环T n(R)(n≥2)是拟正则Armendariz环,并通过例子说明任意环R上的全矩阵环M n(R)(n≥2)不是拟正则Armendariz环。展开更多
提出了一种新的基于人工电磁超材料的宽带MIMO(Multiple-Input Multiple-Output)天线的去耦方法,通过在两个天线单元之间周期性放置开口三角环形谐振器OTRR(Open Triangular Ring Resonator)来降低耦合度。多个不同谐振频率的OTRR有效...提出了一种新的基于人工电磁超材料的宽带MIMO(Multiple-Input Multiple-Output)天线的去耦方法,通过在两个天线单元之间周期性放置开口三角环形谐振器OTRR(Open Triangular Ring Resonator)来降低耦合度。多个不同谐振频率的OTRR有效地增强了去耦带宽,与未加载去耦结构的MIMO天线相比,在5.2 GHz频段,百分比带宽为5.74%,隔离度提高了9 d B以上。展开更多
文摘Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.
基金Foundation item： Supported by the Fund of Beijing Education Committee（KM200610005024） Supported by the National Natural Science Foundation of China（10671061）
文摘We consider the sufficient and necessary conditions for the formal triangular matrix ring being right minsymmetric, right DS, semicommutative, respectively.
基金The National Natural Science Foundation of China(No.10971024)the Specialized Research Fund for the Doctoral Program of Higher Education(No.200802860024)the Natural Science Foundation of Jiangsu Province(No.BK2010393)
文摘An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.
文摘In this paper we study the formal triangular matrix ring T =and give some necessary and sufficient conditions for T to be (strongly) separative, m-fold stable and unit 1-stable. Moreover, a condition for finitely generated projec-tive T-modules to have n in the stable range is given under the assumption that A and B are exchange rings.
基金Partially supported by the Fund (KM200610005024) of Beijing Education Committeethe NNSF (10671061) of China.
文摘In this paper the sufficient and necessary conditions are given for a formal triangular matrix ring to be right PP, generalized right PP, or semihereditary, respectively.
基金The NNSF(10571026)of Chinathe Specialized Research Fund(20060286006)for the Doctoral Program of Higher Education.
文摘A ring R is said to be right McCoy if the equation f（x）g（x） = 0, where y（x） and g（x） are nonzero polynomials of R[x], implies that there exists nonzero s E R such that f（x）s = 0. It is proven that no proper （triangular） matrix ring is one-sided McCoy. It is shown that for many polynomial extensions, a ring R is right Mccoy if and only if the polynomial extension over R is right Mccoy.
基金The Foundation for Excellent Doctoral Dissertationof Southeast University (NoYBJJ0507)the National Natural ScienceFoundation of China (No10571026)the Natural Science Foundation ofJiangsu Province (NoBK2005207)
文摘The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.
文摘提出了一种新的基于人工电磁超材料的宽带MIMO(Multiple-Input Multiple-Output)天线的去耦方法,通过在两个天线单元之间周期性放置开口三角环形谐振器OTRR(Open Triangular Ring Resonator)来降低耦合度。多个不同谐振频率的OTRR有效地增强了去耦带宽,与未加载去耦结构的MIMO天线相比,在5.2 GHz频段,百分比带宽为5.74%,隔离度提高了9 d B以上。
