具有高阶分界线环的多项式微分系统的近似系统

利用Hamilton系统的挑动系统得到了构造具有高阶分界线环的多项式微分系统的近似系统的一种方法，并举出了具体例子．     

具有十个大振幅极限环的五次多项式系统

本文研究一类五次平面多项式系统赤道极限环分支问题.运用奇点量方法,首次证明了五次多项式系统可在赤道分支出十个极限环.     

具有色多项式的图

本文讨论了色多项式为的图的结构,给出了具有这种色多项式的全部色等价图.     

多项式环上的投射模

本文证明了：如果R为交换的w-遗传环，则有限生成的投射R[x1…xn]-模能够从R扩张，进而系统研究了非Noether环上多项式环上的模结构．     

M-McCoy环和M-Armendariz环的多项式扩张

研究非交换环上的相对于幺半群的McCoy环和Armendariz环的多项式扩张.对于包含无限循环子幺半群的交换可消幺半群M,证明了若R是M-McCoy（或M-Armendariz）环,则R上的洛朗多项式环R[x,x-1]是M-McCoy（或M-Armendariz）环.     

平坦的多项式剩余类环

本文证明了如果多项式的剩余类环 A=R[T]/fR[T]作为 R-模是平坦模,且R是约化环,则f是正规多项式.特别地,若R还是连通的,则f的首项系数是单位.也证明了弱整体有限的凝聚环是约化环,以及弱整体为有限的凝聚连通环是整环.     

关于Bernstein多项式

<正> 对于任意的光滑模函数ω(t)他们没有证明相应的定理.因此,人们自然要问这些定理对更广的函数类是否成立?本文的目的是将上述定理改进为 定理1 设φ(t)>0(01     

Division Closed Lattice-Ordered Rings

In this note we consider properties of unital lattice-ordered rings that are division closed and characterize unital lattice-ordered algebras that are algebraic and division closed. Extending partial orders to lattice orders that are division closed is also studied. In particular, it is shown that a field is L ^? if and only if it is O ^?.     

Lattice-Ordered Matrix Rings Over Totally Ordered Rings

For an n ×n matrix algebra over a totally ordered integral domain, necessary and sufficient conditions are derived such that the entrywise lattice order on it is the only lattice order (up to an isomorphism) to make it into a lattice-ordered algebra in which the identity matrix is positive. The conditions are then applied to particular integral domains. In the second part of the paper we consider n ×n matrix rings containing a positive n-cycle over totally ordered rings. Finally a characterization of lattice-ordered matrix ring with the entrywise lattice order is given.     

格序环的一个根的结构

从不同角度刻画了格序环Ｒ的Ｐ－根和ｌ－Ｂ根，并对ｌ－Ｑ根环进行了讨论．揭示了Ｒ及Ｒ上的全矩阵环Ｒｎ的ｌ－Ｑ根，ｌ－Ｑ理想，素ｌ－理想，半素ｌ－理想之间的关系．     

Recognition of Lattice-Ordered Matrix Rings

For an ?-unital ?-ring R, various recognition criteria are given for R to be isomorphic to a matrix ?-ring over an ?-unital ?-ring with the entrywise order.     

格序环的根

讨论格序环中诣零单侧l-理想的幂零性,证明了许多满足特殊格序环等式的环的所有根相同．     

On Automorphisms of Polynomial Rings

Implicit in the work of Lane [1] is the result that if k isan algebraically closed field then every k-automorphism leavesa non-zero proper ideal of k[x, y] invariant. The purpose ofthis note is to show that this result does not hold for k[x,y, z].     

Lattice-Ordered Matrix Rings Over the Integers

We show that the only compatible lattice order on a matrix ring over the integers for which the identity matrix is positive is (up to isomorphism) the usual, entrywise, lattice order. We also find a condition that guarantees that the only compatible lattice order on a matrix ring over the integers is formed by multiplying the positive cone of the usual, entrywise, lattice order by a matrix with positive entries. Using this condition, we show that such orders are the only compatible ones in the two-by-two case.     

On Primitive Ideals in Polynomial Rings over Nil Rings

Let R be a nil ring. We prove that primitive ideals in the polynomial ring R[x] in one indeterminate over R are of the form I[x] for some ideals I of R. Presented by S. MontgomeryMathematics Subject Classifications (2000) 16N40, 16N20, 16N60, 16D25.Agata Smoktunowicz: Current address: Institute of Mathematics, Polish Academy of Sciences, 00-956 Warsaw 10, niadeckich 8, P.O. Box 21, Poland.     

On Unimodular Rows over Polynomial Rings

Let A be a commutative ring and n 3 a positive integer. In this paper, we consider unimodular rows (f₁(x),..., f_n(x)) over A[x]. We prove that, if the row of the leading coefficients of f_i(x) is unimodular over A and a A, then there exists E_n(A[x]) such that (f₁(x),...,f_n(x)) = (f₁(a),...,f_n(a)). Also, if A is a Noetherian ring with finite Krull dimension and the row of leading coefficients satisfies the same condition, then we give a bound for the length of in terms of elementary transvections.Partially supported by INTAS 93–436EXT and DFG–RFBR grant No. 96–01–00092G.2000 Mathematics Subject Classification: 19A13, 19B14, 13C10, 13B25, 13F20