罗朗级数环的主拟Baer性

称环 R为右主拟 Baer环（简称为右p·q.Baer环）,如果 R的任意主右理想的右零化子可由幂等元生成.本文证明了,若环 R满足条件Sl（R）（?）C（R）,则罗朗级数环R[[x,x-1]]是右p.q.Baer环当且仅当R是右p.q.Baer环且R的任意可数多个幂等元在I（R）中有广义join.同时还证明了,R是右p.q.Baer环当且仅当R[x,x-1]是右P.q.Baer环.     

Malcev-Neumann环的主拟Baer性质

设R是环，G是偏序群，σ是从G到R的自同构群的映射。本文研究了Malcev-Neumann环R*((G))是主拟Baer环的条件。证明了如下结果：如果R是约化环并且σ是弱刚性的，则R*((G))是主拟Baer环当且仅当R是主拟Baer环，并且I(R)的任意G可标子集在I(R)中具有广义并．     

迭代的斜多项式环的Baer和拟-Baer性

本文主要讨论了环R和迭代的斜多项式环T(u)的零化子之间的关系,从而得出在一定条件下,R是Baer环当且仅当T(u)是Baer环。而对于拟-Baer性,只要R是拟Baer环就行了,作为推论我们证明了sl(2)的包络代数和量子包络代数都是拟Baer环。     

广义幂级数环的拟Baer性

设R是环,（S,≤）是严格全序幺半群,且对任意s∈S都有0≤s.本文证明了环R是拟Baer环当且仅当R上的广义幂级数环[[RS,≤]]是拟 Baer环.     

广义幂级数环的拟Baer性

设R是环,(S,≤)是严格全序幺半群,且对任意s∈S都有0≤s.本文证明了环R是拟Baer环当且仅当R上的广义幂级数环[RS,≤]]是拟Baer环。     

关于Baer PP和PS环的一些性质(英)

在此文中,我们对Strong-Armendariz环和Baer PP及PS环Ore-扩张R[x,x~(-1)；α]的一些性质进行了讨论研究,并得到了一些结果．主要证明了R是Baer(PP)环当且仅当R[[x]]是Baer(PP)环及R是α-rigid环时,R是Baer(PP,PS)环当且仅当R[[x]]是Baer(PP,PS)环．     

(α,δ)-弱刚性环上的Ore扩张（英文）

本文研究(α,δ)-弱刚性环上的Ore扩张环R[x;α,δ]的弱对称性、弱zip性、幂零p.p.性和幂零Baer性.利用对多项式的逐项分析的方法,证明了如果R是(α,δ)-弱刚性环和半交换环,则Ore扩张环R[x;α,δ]是弱对称的(弱zip的,幂零p.p.的,幂零Baer的)当且仅当R是弱对称的(弱zip的,幂零p.p.的,幂零Baer的).这些结果统一和扩展了前面已有的相关结论.     

APT环上幂等阵的对角化

设R是一阿贝尔环(R的所有幂等元都在中心里),A是R上的一幂等阵.本文证明了以下结果：(a)A相抵于一对角阵当且仅当A相似于一对角阵;(b)若R是一APT(阿贝尔投射平凡)环,则A在相似变换之下可唯一地化为对角形diag{e₁, ..., e_n｝,这里e_i整除e_i+1;(c)R是APT环当且仅当R/I是APT环,这里I是环R的一幂零理想.由(a),还证明了分离的阿贝尔正则环是APT环.     

多项式环的单位和稳定度的注记(英文)

称环R为广义2-素环,如果R的幂零元集与上诣零根一致.证明了R上的多项式为单位当且仅当它的常数项是R中的单位而其它系数是幂零的.因此,广义2-素环上的多项式环的稳定度大于一.     

Noether环上的幂稳定自由模

设I是Noether环R的投射理想, I^m=Iⁿ, m≠n. 该文证明, 有限生成投射右R - 模幂稳定自由当且仅当(1) 存在环S使得I^|m-n|( S ( R且有限生成投射S - 模是幂稳定自由; (2) 有限生成投射右R/I^|m-n| - 模幂稳定自由.     

On inverse skew Laurent series extensions of weakly rigid rings

Let R be a ring equipped with an automorphism α and an α-derivation δ. We studied on the relationship between the quasi Baerness and (α, δ)-quasi Baerness of a ring R and these of the inverse skew Laurent series ring R((x^?1; α, δ)), in case R is an (α, δ)-weakly rigid ring. Also we proved that for a semicommutative (α, δ)-weakly rigid ring R, R is Baer if and only if so is R((x^?1; α, δ)). Moreover for an (α, δ)-weakly rigid ring R, it is shown that the inverse skew Laurent series ring R((x^?1; α, δ)) is left p.q.-Baer if and only if R is left p.q.-Baer and every countable subset of left semicentral idempotents of R has a generalized countable join in R.     

I半π正则环

Let R be a ring and I an ideal of R.A ring R is called I-semi-π-regular if R/I isπ-regular and idempotents of R can be strongly lifted modulo I.Charac- terizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored.     

Rickart Modules

The concept of right Rickart rings (or right p.p. rings) has been extensively studied in the literature. In this article, we study the notion of Rickart modules in the general module theoretic setting by utilizing the endomorphism ring of a module. We provide several characterizations of Rickart modules and study their properties. It is shown that the class of rings R for which every right R-module is Rickart is precisely that of semisimple artinian rings, while the class of rings R for which every free R-module is Rickart is precisely that of right hereditary rings. Connections between a Rickart module and its endomorphism ring are studied. A characterization of precisely when the endomorphism ring of a Rickart module will be a right Rickart ring is provided. We prove that a Rickart module with no infinite set of nonzero orthogonal idempotents in its endomorphism ring is precisely a Baer module. We show that a finitely generated module over a principal ideal domain (PID) is Rickart exactly if it is either semisimple or torsion-free. Examples which delineate the concepts and results are provided.     

Principally Quasi-Baer skew Generalized Power Series modules

Let R be a ring and S a strictly totally ordered monoid. Let ω: S → End(R) be a monoid homomorphism. Let M _R be an ω-compatible module and either R satisfies the ascending chain conditions (ACC) on left annihilator ideals or every S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join. We show that M _R is p.q.-Baer if and only if the generalized power series module M[[S]] _{R[[S, ω]]} is p.q.-Baer. As a consequence, we deduce that for an ω-compatible ring R, the skew generalized power series ring R[[S, ω]] is right p.q.-Baer if and only if R is right p.q.-Baer and either R satisfies the ACC on left annihilator ideals or any S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join in R. Examples to illustrate and delimit the theory are provided.     

Principally Quasi-Baer Skew Power Series Rings

Let α be an endomorphism of R which is not assumed to be surjective and R be α-compatible. It is shown that the skew power series ring R[[x; α]] is right p.q.-Baer if and only if the skew Laurent series ring R[[x, x ^?1; α]] is right p.q.-Baer if and only if R is right p.q.-Baer and every countable subset of right semicentral idempotents has a generalized countable join. Examples to illustrate and delimit the theory are provided.     

左非奇异左CS-环和左遗传左CS-环

本文首先证明了：环为左非奇异左CS-环当且仅当它为左余非奇异Baer环,然后给出左遗传左CS-环,正则左遗传左CS-环和左遗传左连续环的某些刻划.