广义幂级数环上的PS模

Let R be a commutative ring and(S,≤)a strictly totally ordered monoid which satisfies the condition that 0≤s for every s ∈ S,In this paper we show that if RM is a PS-module,then the module [[M^s,≤]]of generalized power series over M is a PS [[R^s,≤]]-module.     

Triangular Matrix Representations of Rings of Generalized Power Series

Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either （S,≤） satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]].     

A Note on Generalized Long Mo dules

Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB （S（π）） where the opposite group S（π） of the semidirect product of the opposite group πopof a group π by π. As an application, we show that this is a Turaev braided group-category HLBfor a quasitriangular Turaev group-coalgebra H and a coquasitriangular Turaev group-algebra B.     

Principal Quasi-Baerness of Rings of Skew Generalized Power Series

Let R be a ring and （S, 〈） be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any S-indexed subset of S,（R） has a generalized join in S,（R）. Several known results follow as consequences of our results.     

Zip模(英文)

A ring R is called right zip provided that if the annihilator τR（X） of a subset X of R is zero, then τR（Y） = 0 for some finite subset Y C X. Such rings have been studied in literature. For a right R-module M, we introduce the notion of a zip module, which is a generalization of the right zip ring. A number of properties of this sort of modules are established, and the equivalent conditions of the right zip ring R are given. Moreover, the zip properties of matrices and polynomials over a module M are studied.     

广义幂级数代数的滤链维数

In this paper, we study the properties of generalized power series modules and the filtration dimensions of generalized power series algebras. We obtain that [[△S,≤]]- gfd([[AS,≤]]) =△-gfd(A) if A is an R-module where R is a perfect and coherent commutative algebra, and(R, ≤) is standardly stratified.     

Generalized PP and Zip Subrings of Matrix Rings

Let R be an abelian ring. We consider a special subring An, relative to α2,…, αn∈ REnd（R）, of the matrix ring Mn（R） over a ring R. It is shown that the ring An is a generalized right PP-ring （right zip ring） if and only if the ring R is a generalized right PP-ring （right zip ring）. Our results yield more examples of generalized right PP-rings and right ziu rings.     

Principal quasi-Baerness of formal power series rings

Let R be a ring. We consider left （or right） principal quasi-Baerness of the left skew formal power series ring R[[x;α]] over R where a is a ring automorphism of R. We give a necessary and sufficient condition under which the ring R[[x; α]] is left （or right） principally quasi-Baer. As an application we show that R[[x]] is left principally quasi-Baer if and only if R is left principally quasi- Baer and the left annihilator of the left ideal generated by any countable family of idempotents in R is generated by an idempotent.     

关于FP-内射维数的一个注记

Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR（ω） ∞ implies G-dimω（M） ∞,where M ∈ modR.This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001.In addition,we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when G-dimω（M） is finite.     

Characteristic modules and tensor products over quasi-hereditary algebras

Let A be a monomial quasi-hereditary algebra with a pure strong exact Borel subalgebra B.It is proved that the category of induced good modules over B is contained in the category of good modules over A;that the characteristic module of A is an induced module of that of B via the exact functor-(?)_B A if and only if the induced A-module of an injective B-module remains injective as a B-module.Moreover,it is shown that an exact Borel subalgebra of a basic quasi-hereditary serial algebra is right serial and that the characteristic module of a basic quasi-hereditary serial algebra is exactly the induced module of that of its exact Borel subalgebra.     

相对平坦模的$\aleph$-积

设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中$0\leq A相似文献   

THE GOLDBACH-VINOGRDOV THEOREM WITH THREE PRIMES IN A THIN SUBSET

1.IntroductionandStatementofResultsIn1937,Vinogradovi7]provedthatJ(N),thenumberofrepresefltationsofanilltegerNassumsofthreeprimes,satisfiesthefollowingasymptoticformulawherea(N)isthesingularseries,andu(N)>>1foroddN.Itthereforefollowsthateverysufficientlylargeoddintegeristhesumofthreeprimes.ThissettledtheternaryGoldbachproblem,andtheresultisreferredtoastheGoldbach-Vinogradovtheorein.ManyauthorshaveconsideredthecorrespondingproblemswithrestrictedconditionsposedonthethreeprimesintheGoldbach…     

广义幂级数环上Morita Context环的稳定条件

In this paper, we show that if rings A and B are （s, 2）-rings, then so is the ring of a Morita Context（[[A^S,≤]],[[B^S,≤]],[[M^S,≤]],[[N^S,≤]],ψ^S,Ф^S）of generalized power series. Also we get analogous results for unit 1-stable ranges, GM-rings and rings which have stable range one. These give new classes of rings satisfying such stable range conditions.     

拟-Armendariz模

For a right R-module N, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that NR is quasi-Armendariz if and only if Mm(N)Mm(R) is quasi-Armendariz if and only if Tm(N)Tm(R) is quasi-Armendariz, where Mm(N) and Tm(N) denote the m×m full matrix and the m×m upper triangular matrix over N, respectively. NR is quasi-Armendariz if and only if N[x]R[x] is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.     

标准算子代数上的Jordan映射

Let A be a standard operator algebra on a Banach space of dimension 〉 1 and B be an arbitrary algebra over Q the field of rational numbers. Suppose that M ： A → B and M^＊ ： B → A are surjective maps such that {M（r（aM^＊（x）＋M^＊（x）a））=r（M（a）x＋xM（a））, M^＊（r（M（a）x＋xM（a）））=r（aM^＊（x）＋M^＊（x）a） for all a ∈ A, x ∈ B, where r is a fixed nonzero rational number. Then both M and M^＊ are additive.     

关于$(m,n)$-凝聚模与预包络

In this paper, let m, n be two fixed positive integers and M be a right R-module, we define （m, n）-M-flat modules and （m, n）-coherent modules. A right R-module F is called （m, n）-M-flat if every homomorphism from an （n, m）-presented right R-module into F factors through a module in addM. A left S-module M is called an （m, n）-coherent module if MR is finitely presented, and for any （n, m）-presented right R-module K, Hom（K, M） is a finitely generated left S-module, where S = End（MR）. We mainly characterize （m, n）-coherent modules in terms of preenvelopes （which are monomorphism or epimorphism） of modules. Some properties of （m, n）-coherent rings and coherent rings are obtained as corollaries.     

形式三角矩阵环的PS性质和CESS性质

设$R$是环. 称右$R$-模$M$是PS-模,如果$M$具有投射的socle. 称$R$是PS-环,如果$R_R$是PS-模. 称$M$是CESS-模,如果$M$的任意具有基本socle的子模是$M$的某个直和因子的基本子模.本文给出了形式三角矩阵环 $T=\left( \begin{array}{cc} A & 0 \\     

Frobenius扩张上的$n$-Gorenstein投射模和维数

In this paper, we study n-Gorenstein projective modules over Frobenius extensions and n-Gorenstein projective dimensions over separable Frobenius extensions. Let R ■ A be a Frobenius extension of rings and M any left A-module. It is proved that M is an n-Gorenstein projective left A-module if and only if A ■_RM and Hom_R(A, M) are n-Gorenstein projective left A-modules if and only if M is an n-Gorenstein projective left R-module. Furthermore, when R ■ A is a separable Frobenius extension, n-Gorenstein projective dimensions are considered.     

$(m,d)$-内射盖与Gorenstein $(m,d)$-平坦模

研究了$(m,d)$-内射$R$-模作成的类是(预)盖类的条件,证明了$(m,d)$-凝聚环上的每一个左$R$-模都具有$(m,d)$-内射盖.在此基础上,又引入研究了Gorenstein $(m,d)$-平坦模和Gorenstein $(m,d)$-内射模,证明了$(m,d)$-凝聚环上的左$R$-模$M$是Gorenstein$(m,d)$-平坦模的充分必要条件是它的特征模$M^{+}$是Gorenstein $(m,d)$-内射模.推广了Goresntein平坦模和Goresntein $n$-平坦模上的一些结果.