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1.

《Quaestiones Mathematicae》2013,36(4):451-466

**Abstract**Let

*d*be a positive integer, and

*F*be a field of characteristic zero. Suppose that for each positive integer

*n*,

*I*

_{n}, is a

*GL*

_{n},(

*F*)- invariant of forms of degree

*d*in x

_{1}, …,

*x*

_{n}, over F. We call {

*I*

_{n}} an

*additive family of invariants*if

*I*

_{p+q}(

*f*⊥

*g*) =

*I*

_{p}(

*f*).

*I*

_{q}(

*g*) whenever

*f*;

*g*are forms of degree

*d*over

*F*in

*x*

_{l}, …,

*x*

_{p}; …,

*x*

_{q}respectively, and where (

*f*⊥

*g*)(

*x*

_{l}, …,

*x*

_{p+q}) =

*f*(

*x*

_{1}, …,

*x*

_{p},) +

*g*(

*x*

_{p+1}, …,

*x*

_{p+q}). It is well-known that the family of discriminants of the quadratic forms is additive. We prove that in odd degree d each invariant in an additive family must be a constant. We also give an example in each even degree d of a nontrivial family of invariants of the forms of degree d. The proofs depend on the

*symbolic method*for representing invariants of a form, which we review. 相似文献

2.

《Quaestiones Mathematicae》2013,36(1-2):1-5

**Abstract**A family

*K*of right

*R*-modules is called a natural class if

*K*is closed under submodules, direct sums, infective hulls, and isomorphic copies. The main result of this note is the following: Let

*K*be a natural class on Mod-

*R*and

*M*ε

*K*. If

*M*satisfies a.c.c. (or d.c.c.) on the set of submodules {

*N*?

*M*:

*M/N*ε K}, then each nil subring of End(

*M*) is nilpotent. 相似文献

_{R}3.

《代数通讯》2013,41(9):4267-4275

**Abstract**In Fortes (2001), we introduced a notion of order for associative pairs and we obtained a Goldie-like characterization of left orders in a semiprime pair coinciding with its socle. In this paper, we take up again that notion of order to establish a Faith-Utumi theorem, which studies left orders in a prime pair coinciding with its socle. 相似文献

4.

1.:敲g(x)篇〔一二,二]上之非降的有界缝差两数,业具有性鬓(K)s‘二一0,一。(:);f--:.,。g。尹(:)!d:一郁匕,(‘一”,”;dg)篇在〔一二,司上定羲业且满足修件:,一{户,(柳dg(·)}青<一,>l的可测蝮值函数族{f(幻}.封龄一徊乙“(一二,侧d刃中之子族凌B(幻},若由f(劣)(乙,(一二,二:dg),夕>1生+上夕q=1,及f--:ha”“’“““’一0纷{B(x)}之任何B(哟成立必滇致f(幻在〔一二,司上规乎虚虚等焚零则释{B(x)}在乙“(一二,侧dg)中完全. 函数族的完全性是舆函数横造的一些简题很有阴保的.徙【l]我们知道{e‘”}豁。是在乙,(一二,州dg),,>1,中完全的,… 相似文献

5.

《代数通讯》2013,41(8):2705-2711

Let A be a strong independence algebra of finite rank with at most one constant, and let G he the group of automorphisms of A. Let α be a singular endomorphism of α

^{G}= 〈{α} U*G*〉. We describe the elements of α^{G}and give additional characterisations when A is a proper independence algebra and G is a periodic group. 相似文献6.

In this paper the properties of some maximum fractional [0, κ]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained. 相似文献

7.

《代数通讯》2013,41(8):2809-2825

Let k be a field and A

_{n}(ω) be the Taft's n^{2}-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(A_{n}(ω)) of A_{n}(ω) is a ribbon Hopf algebra. In the previous articles, we constructed an n_{4}-dimensional Hopf algebra H_{n}(p, q) which is isomorphic to D(A_{n}(ω)) if p ≠*0*and q = ω^{−1 }, and studied the irreducible representations of H_{n}(*1*, q) and the finite dimensional representations of H_{3}(*1*, q). In this article, we examine the finite-dimensional representations of H_{n}(*l*q), equivalently, of D(A_{n}(ω)) for any n ≥*2*. We investigate the indecomposable left H_{n}(*1*, q)-module, and describe the structures and properties of all indecomposable modules and classify them when k is algebraically closed. We also give all almost split sequences in mod H_{n}(*1*, q), and the Auslander-Reiten-quiver of H_{n}(*1*q). 相似文献8.

《Quaestiones Mathematicae》2013,36(3-4):289-302

**Abstract**Let d be a positive integer and

*F*be a field of characteristic 0. Suppose that for each positive integer

*n*,

*I*

_{n}is a polynomial invariant of the usual action of

*GL*on Λ

_{n}(F)^{d}(F

^{n}), such that for

*t*ϵ Λ

^{d}(

*F*

^{k}) and s ϵ Λ

^{d}(

*F*

^{l}),

*I*

_{k + l}(t

*l*s) =

*I*

_{k}(t)

*I*

_{t}

*(s)*, where

*t*⊥

*s*is defined in §1.4. Then we say that

*{I*is an additive family of invariants of the skewsymmetric tensors of degree

_{n}}*d*, or, briefly, an additive family of invariants. If not all the

*I*are constant we say that the family is non-trivial. We show that in each even degree

_{n}*d*there is a non-trivial additive family of invariants, but that this is not so for any odd

*d.*These results are analogous to those in our paper [3] for symmetric tensors. Our proofs rely on the symbolic method for representing invariants of skewsymmetric tensors. To keep this paper self-contained we expound some of that theory, but for the proofs we refer to the book [2] of Grosshans, Rota and Stein. 相似文献

9.

《Quaestiones Mathematicae》2013,36(3):293-300

**Abstract**If G is the group of homeomorphisms of the rationals with usual topology and H ⋚ G is such that |G:H| < 2

^{x0}then there exists a finite, non-empty subset Y of the rational numbers such that G(Y) ⋚ H ⋚ G

^{{Y}}where G(Y) is the group o all homeomorphisms in G fixing a neighbourhood of Y and G

^{{Y}}is the set-wise stabilizer of Y in G. 相似文献

10.

In this paper, we are concerned with the existence of periodic solutions of second-order non-autonomous systems. By applying the Schauder''s fixed point theorem and Miranda''s theorem, a new existence result of periodic solutions is established. 相似文献

11.

12.

《Quaestiones Mathematicae》2013,36(1-3):235-243

A connector

*U*on a space*S*is a function from*S*to the power set of S such that each*x*in s belongs to its image. The image of x is denoted by*xU.*In other words, the relation {(x,y): y ϵ*xU*,*x ϵ S*) is a reflexive binary relation. A space with a certain set of connectors is a generalization of topological spaces as well as uniform spaces. In this paper, a notion of completeness of such a space is introduced. This completeness corresponds to completeness of uniform spaces if a set of cannectors meets the conditions of uniformity. Compactness of topological Spaces is a special case of the completeness. 相似文献13.

<正> 设函数w在单位圆 E_z:|z|<1上是正则的.假如f(z)在 E_z上是单叶的,那末 D_f=f(E_z)是 w 平面上单叶的区域.记这种单叶函数f(z)的全体为 S_p,S_1=S.若 D_f 以原点 w=0 为星形中心,就是说若 w_0∈D_f则缐段■整个地落在区域 D_f 中,称这种函数 f(z)是 E_z 中的星像函数,其特徵是在 E_z 相似文献

14.

Dolph Ulrich 《Mathematical Logic Quarterly》1992,38(1):321-323

C5.ω is obtained by adding, schematically, to the strict-implicational fragment C5 of S5 the axiom ((

*p*→*q*) → (*q*→*p*)) → (*q*→*p*). This paper presents a fully general proof that neither C5.ω nor any of a descending chain of its extensions is complete with respect to any class of frames, correcting the garbled details of a version skeched in an earlier paper (same Zeitschrift 31 (1985), 201-208). 相似文献15.

16.

PROPERTIES OF CHARACTERISTIC FUNCTIONS AND EXISTENCE OF LIMIT CYCLES OF LIENARD''S EQUATION

*下载免费PDF全文* Chen Xiudong 《数学年刊B辑(英文版)》1983,4(2):207-216

In this paper, the author considers Lienard''s equation, studies the properties of so-called characteristic functions and gives three theorems which ensure that the equation has at least one limit cycle. The theorems generlize Filippov''s Theorem which is a repesentative result, Dragilev''s Theorem, Theorem 1 2 of [6], Theorem 9 of [8] and Theorems 1, 2 of [9] respectively. 相似文献

17.

《Quaestiones Mathematicae》2013,36(1-4):339-347

**Abstract**An improved bound is given for the index of nil-potency of a finitely generated nil ring of index n in terms of the index of nilpotency of the ideal generated by T

^{m}where m = [n/2] and T is a m-subset of the set of generators. If m = 3 it is proved that T

^{10}is contained in an ideal generated by twenty-seven cubes and this is applied to get bounds for the index of nilpotency of a finitely generated nil ring of index 6 or 7, bounds which are less than one hundredth of the bounds we obtained in a previous paper. 相似文献

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