I-提升模的有限直和

I-提升模的直和不一定是I-提升模.本文给出了使I-提升模的直和仍是I-提升模成立的条件,即证明了当M=M1⊕M2,其中M1和M2是I-提升的.如果Mi是Mj-投射的（i,j=1,2）或M是duo模,则M是I-提升的.     

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．     

主拟-Baer模

In this paper, we give the equivalent characterizations of principally quasi-Baer modules, and show that any direct summand of a principally quasi-Baer module inherits the property and any finite direct sum of mutually subisomorphic principally quasi-Baer modules is also principally quasi-Baer. Moreover, we prove that left principally quasi-Baer rings have Morita invariant property. Connections between Richart modules and principally quasi-Baer modules are investigated.     

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。     

斜幂级数环的主拟Baer性

设R是环,并且R的左半中心幂等元都是中心幂等元, α是R的一个弱刚性自同态. 本文证明了斜幂级数环R[[x,α]]是右主拟Baer环当且仅当R是右主拟Baer环,并且R的任意可数幂等元集在I(R)中有广义交,其中I(R)是R的幂等元集.     

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.     

支撑τ-倾斜模和支撑倾斜模

设∧是一个有限维代数.本文证明了任意支撑倾斜∧-模是支撑τ-倾斜∧-模.反之,任意投射维数小于等于1的支撑τ-倾斜∧-模是支撑倾斜∧-模.特别地,如果∧是遗传的,则任意支撑倾斜∧-模恰好是支撑τ-倾斜∧-模.     

半模的投射盖和半模的根

引入了半模的投射盖和半模的根的初步的定义，给出了半模范畴中投射盖和根的几个初步的结果，推广了模的投射盖和根的一些性质．     

关于ann-内射模和ann-平坦模

左R—模E是ann—内射的。如果对于R的每个有限生成右零化子理想r(L)到R的R—模同态都能延拓为到E的R—模同态.同样,我们称左R—模M是ann—平坦的如果对于R的每个有限生成右零化子理想r (L),都可以得到正合列0→r(L)⊕_RM→R__R⊕M.在本文中,我们证明了R—模B是ann—平坦的当且仅当它的示性模B~·=Hom_R(B,Q/Z)是ann—内射的.     

相关于遗传挠理论的平坦模和ML模

本文引入了相关于遗传挠理论的平坦模和 ML 模,利用它们刻划了相关 Coherent环,相关 noether 环以及半遗传环,并使得[3]中主要定理和命题有了更完美的形式,此外,我们还给出了平坦模是τ—平坦模、fg τ—平坦模是投射模的条件。     

Modules having Baer summands

Let R be an arbitrary ring with identity and M a right R-module with S = End_R(M). Let F be a fully invariant submodule of M and I^?1(F) denotes the set {m∈M:Im?F} for any subset I of S. The module M is called F-Baer if I^?1(F) is a direct summand of M for every left ideal I of S. This work is devoted to the investigation of properties of F-Baer modules. We use F-Baer modules to decompose a module into two parts consists of a Baer module and a module determined by fully invariant submodule F, namely, for a module M, we show that M is F-Baer if and only if M = F⊕N where N is a Baer module. By using F-Baer modules, we obtain some new results for Baer rings.     

Feebly Baer Rings and Modules

A right module M over a ring R is called feebly Baer if, whenever xa = 0 with x ∈ M and a ∈ R, there exists e² = e ∈ R such that xe = 0 and ea = a. The ring R is called feebly Baer if R_R is a feebly Baer module. These notions are motivated by the commutative analog discussed in a recent paper by Knox, Levy, McGovern, and Shapiro [6 Knox , M. L. , Levy , R. , McGovern , W. Wm. , Shapiro , J. ( 2009 ) Generalizations of complemented rings with applications to rings of functions. . J. Alg. Appl. 8 ( 1 ): 17 – 40 .[Crossref] , [Google Scholar]]. Basic properties of feebly Baer rings and modules are proved, and their connections with von Neumann regular rings are addressed.     

On Weak Dual Rickart Modules and Dual Baer Modules

We introduce and study the notion of wd-Rickart modules (i.e. modules M such that for every nonzero endomorphism ? of M, the image of ? contains a nonzero direct summand of M). We show that the class of rings R for which every right R-module is wd-Rickart is exactly that of right semi-artinian right V-rings. We prove that a module M is dual Baer if and only if M is wd-Rickart and M has the strong summand sum property. Several structure results for some classes of wd-Rickart modules and dual Baer modules are provided. Some relevant counterexamples are indicated.     

A solution to the Baer splitting problem

Let be a commutative domain. We prove that an -module is projective if and only if for any torsion module . This answers in the affirmative a question raised by Kaplansky in 1962.

     

Perfect Baer Subplane Partitions and Three-Dimensional Flag-Transitive Planes

The classification of perfectBaer subplane partitions of PG(2, q²) is equivalentto the classification of 3-dimensional flag-transitive planeswhose translation complements contain a linear cyclic group actingregularly on the line at infinity. Since all known flag-transitiveplanes admit a translation complement containing a linear cyclicsubgroup which either acts regularly on the points of the lineat infinity or has two orbits of equal size on these points,such a classification would be a significant step towards theclassification of all 3-dimensional flag-transitive planes. Usinglinearized polynomials, a parametric enumeration of all perfectBaer subplane partitions for odd q is described.Moreover, a cyclotomic conjecture is given, verified by computerfor odd prime powers q < 200, whose truth would implythat all perfect Baer subplane partitions arise from a constructionof Kantor and hence the corresponding flag-transitive planesare all known.     

Monomial Modules and Endo-Monomial Modules

We determine the multiplicity algebras and multiplicity modules of a p-monomial module. For a general p-group P, we find a sufficient and necessary condition for an endo-monomial P-module to be an endo-permutation P-module, and prove that a capped indecomposable endo-monomial P-module is of p ^′-rank. At last, we give an alternative definition of the generalized Dade P-group.     

On the Baer Criterion for Acts Over Semigroups

It is known that although the Baer Criterion for injectivity holds for modules over rings with unit, it is not true for acts over an arbitrary monoid.

Seeking a characterization for the Baer Criterion to hold for acts over a monoid, in this article, using the notion of completeness introduced by Giuli, we find some classes of monoids such that for acts over them the Baer Criterion holds.     

Quasiregular and Baer lattices — II

Let L be a compactly generated multiplicative lattice with 1 compact in which every finite product of compact elements is compact and u ∈ L be a radical element. Under this hypothesis, in this paper we extend the concepts such as Baer lattices, quasiregular lattices etc. to what we respectively call Baer lattices w.r.t. u, quasiregular lattices w.r.t. u etc. and using these concepts we extend here the results proved by D. D. Anderson, C. Jayaram and P. A. Phiri. In the course of the development, we add many fruitful concepts and results. Also we study nature and characterizations of different elements.      

Groups whose proper subgroups are Baer groups

In this paper we classify infinite soluble minimal non-nilpotent-groups, detemine the basic structure of infinite soluble minimal non-Baer-groups, and using famed Heineken-Mohamed-groups we construct an example of minimal non-Baer-group which is not minimal non-nilpotent-group.The author would like to thank Chen Zhangmu and Shi Wuje for narm help and useful advice.