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1.
研究了拟正则半环上的同余,给出了拟正则半环上一类理想的性质,并利用这类理想给出了拟正则半环上可除半环同余的几种等价形式.  相似文献   

2.
研究了一类广义正则半环的理想,利用这类理想,得到了这类半环上同余的几种刻画.  相似文献   

3.
考虑差分方程xn+1=a+b0xn+b1xn-1+…+bk-1xn-(k-1)xn-k其中a,bi是非负实数,a+∑k-1i=0bi>0,k∈{1,2,…}.证明了当k+1为素数时,方程的任半环不超过(2k+2)项;当k+1为合数且只有一个bi≠0时,方程的任半环不超过2k+1+km+0 1项,其中m0=min{m m为k+1的大于1的因数}.结果部分回答了C.Darwen and W.T.Patula提出的公开问题.  相似文献   

4.
引入可除半环的伪理想,它与同余互相唯一决定,在可除半环中利用理想作商是可行的,并证明了同态基本定理.  相似文献   

5.
We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant ellipse.More precisely,a quadratic system having an invariant ellipse can be written into the form x=x2+y2-1+y(ax+by+c),y=x(ax+by+c),and the ellipse becomes x2+y2=1.We prove that(i) this quadratic system is analytic integrable if and only if a=0;(ii) if x2+y2=1 is a periodic orbit,then this quadratic system is Liouvillian integrable if and only if x2+y2=1 is not a limit cycle;and(iii) if x2+y2=1 is not a periodic orbit,then this quadratic system is Liouvilian integrable if and only if a=0.  相似文献   

6.
给出了广义模糊子半环的广义模糊双(内)理想的概念.运用截集、模糊子集的和与积得到了广义模糊子半环的广义模糊双(内)理想的等价条件及性质,同时还得到了在半环的同态映射下同态像及同态原像的性质.当λ=0,μ=1时,得到一般意义下的模糊子半环的模糊双(内)理想的相应结果.  相似文献   

7.
考虑中立型差分方程Δ(xn+pnxn- l) +qnxn- k=0 ,  n=0 ,1 ,2 ,… ,其中 { pn} ,{ qn}为非负实数列 ,qn>0 .k,l为非负整数 k>l,本文给出其任一解的正、负半环的项数的若干上界估计 .  相似文献   

8.
Let u=u(x,t,uo)represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt+δux+γHuxx+βuxxx+f(u)x=αuxx,u(x,0)=uo(x), whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f(0)=0,|f(u)|→∞as |u|→∞,and f∈C^1(R),and there exist the following limits Lo=lim sup/u→o f(u)/u^3 and L∞=lim sup/u→∞ f(u)/u^5 Suppose that the initial function u0∈L^I(R)∩H^2(R).By using energy estimates,Fourier transform,Plancherel's identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv(xxt)+δvx+γHv(xx)+βv(xxx)=αv(xx),v(x,0)=vo(x), the author justifies the following limits(with sharp rates of decay) lim t→∞[(1+t)^(m+1/2)∫|uxm(x,t)|^2dx]=1/2π(π/2α)^(1/2)m!!/(4α)^m[∫R uo(x)dx]^2, if∫R uo(x)dx≠0, where 0!!=1,1!!=1 and m!!=1·3…(2m-3)…(2m-1).Moreover lim t→∞[(1+t)^(m+3/2)∫R|uxm(x,t)|^2dx]=1/2π(x/2α)^(1/2)(m+1)!!/(4α)^(m+1)[∫Rρo(x)dx]^2, if the initial function uo(x)=ρo′(x),for some functionρo∈C^1(R)∩L^1(R)and∫Rρo(x)dx≠0.  相似文献   

9.
刘玉记 《工科数学》2000,16(4):10-16
考虑中立型差分方程△(xn+pnxn-l)+qnxn-k=0,n=0,1,2,…,其中{pn},{qn}为非负实数列,qn&;gt;0,k,l为非负整数k&;gt;l,本文给出其任一解的正、负半环的项数的若干上界估计。  相似文献   

10.
设R是一个咎征非2的素环,U是R的一个平方封闭的李理想,d1,d2,d是R的导子,δ是R的广义导子.本文证明了U为中心李理想,如果以下条件之一成立:(1)d(x)od(y)=xoy;(2)d(x)οd(y)+xοy=0;(3)d1(x)οd2(可)=0;(4)δ([x,y])=0;(5)δ(xοy)=0对所有的x,y∈U.  相似文献   

11.
An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal ideal,and maximal ideal of an ordered semiring,simple ordered semirings,etc.,are introduced.Some properties of them are given and characterizations for minimal ideals are established.Also,the matrix semiring over an ordered semiring is consid-ered.Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups,and on the matrix semiring over a semiring.  相似文献   

12.
A semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. A bounded semiring is a semiring equipped with a compatible bounded partial order. In this paper, properties of zero divisors and prime elements of a bounded semiring are studied. In particular, it is proved that under some mild assumption, the set Z(A) of nonzero zero divisors of A is A / {0, 1}, and each prime element of A is a maximal element. For a bounded semiring A with Z(A) = A / {0, 1}, it is proved that A has finitely many maximal elements if ACC holds either for elements of A or for principal annihilating ideals of A. As an application of prime elements, we show that the structure of a bounded semiring A is completely determined by the structure of integral bounded semirings if either |Z(A)| = 1 or |Z(A)| -- 2 and Z(A)2 ≠ 0. Applications to the ideal structure of commutative rings are also considered. In particular, when R has a finite number of ideals, it is shown that the chain complex of the poset I(R) is pure and shellable, where I(R) consists of all ideals of R.  相似文献   

13.
In Section 2 of the present paper, we introduce the concept of pseudocomplementation for semirings and show the semiring version of some known results in lattice theory. We also introduce semirings with pc-functions and prove some interesting results for minimal prime ideals of such semirings. In Section 3, some classical results for minimal prime ideals in ring theory are generalized in the context of semiring theory.  相似文献   

14.
朱天民  赵小鹏 《大学数学》2007,23(5):119-123
研究了加法半群为半格的半环类S+l中的乘法带半环和矩形带半环类BR中的乘法带半环;给出了ID半环中乘法带半环的结构定理,即ID∩.■°D=.■z∨.■z∨D.  相似文献   

15.
满足a+ab=a+b的幂等半环的结构   总被引:1,自引:0,他引:1  
本文讨论了满足a+ab=a+b的幂等半环的结构,给出这种幂等半环是左零半环的伪强右正规幂等半环,并得出这种幂等半环与环的直积是左环的伪强右正规幂等半环.  相似文献   

16.
Il'in  S. N. 《Mathematical Notes》2001,70(3-4):329-336
Necessary and sufficient conditions for the regularity of complete matrix semirings over an arbitrary semiring are obtained.  相似文献   

17.
半环半直积的同构定理   总被引:1,自引:0,他引:1  
半群半直积及封闭性刻划于文[1],为将半直积的研究推广至半环中,本文首先在交换半环与交换半群的直积上定义加法及乘法运算,从而构造了一类半环;半环半直积.并讨论了半环半直积的同构等问题.  相似文献   

18.
坡上矩阵可逆的条件   总被引:2,自引:0,他引:2  
段俊生 《数学进展》2006,35(3):285-288
坡S是一个元素满足条件s 1=1的交换半环.证明了坡S上n×n矩阵A可逆当且仅当∑k=1 n aik=1(i=1,2,…,n)且aikajk=0(i≠j,k=1,2,…,n).在坡S中可定义补元,得到S上每一个可逆矩阵是一个置换矩阵当且仅当S不包含不同于0和1的有补元.  相似文献   

19.
F. Pastijn 《Semigroup Forum》1983,26(1):151-166
In [2] it is shown that every idempotent distributive semiring is the P?onka sum of a semilattice ordered system of idempotent distributive semirings which satisfy the generalized absorption law x+xyx+x=x. We shall show that an idempotent distributive semiring which satisfies the above absorption law must be a subdirect product of a distributive lattice and a semiring which satisfies the additional identity xyx+x+xyx=xyx. Using this, we construct the lattice of all equational classes of idempotent distributive semirings for which the two reducts are normal bands.  相似文献   

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