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61.
Akalu Tefera Aklilu Zeleke 《International Journal of Mathematical Education in Science & Technology》2013,44(8):1091-1096
In this note we present a class of functions (f, g) that satisfy ‘freshman rules’ in calculus. 相似文献
62.
Lambek extended the usual commutative ideal theory to ideals in noncommutative rings, calling an ideal A of a ring R symmetric if rst ∈ A implies rts ∈ A for r, s, t ∈ R. R is usually called symmetric if 0 is a symmetric ideal. This naturally gives rise to extending the study of symmetric ring property to the lattice of ideals. In the process, we introduce the concept of an ideal-symmetric ring. We first characterize the class of ideal-symmetric rings and show that this ideal-symmetric property is Morita invariant. We provide a method of constructing an ideal-symmetric ring (but not semiprime) from any given semiprime ring, noting that semiprime rings are ideal-symmetric. We investigate the structure of minimal ideal-symmetric rings completely, finding two kinds of basic forms of finite ideal-symmetric rings. It is also shown that the ideal-symmetric property can go up to right quotient rings in relation with regular elements. The polynomial ring R[x] over an ideal-symmetric ring R need not be ideal-symmetric, but it is shown that the factor ring R[x]/xnR[x] is ideal-symmetric over a semiprime ring R. 相似文献
63.
We have described the structure of Q n (G) = Δ n (G)/Δ n+1(G) for 35 particular classes of groups G with order 25 in the previous article. In this article, the structure of Q n (G) for all the remaining classes of groups G with order 25 are presented. 相似文献
64.
We introduce a notion of left nonsingularity for alternative rings and prove that an alternative ring is left nonsingular if and only if every essential left ideal is dense, if and only if its maximal left quotient ring is von Neumann regular (a Johnson-like Theorem). Finally, we obtain a Gabriel-like Theorem for alternative rings. 相似文献
65.
E. van Wickeren 《Numerical Functional Analysis & Optimization》2013,34(1-2):147-180
The main purpose of this paper is to give a proof of quantitative resonance and condensation principles via Baire category arguments in contrast to the gliding hump method used previously. Thereby a new nonquantitative resonance principle is established which is concerned with dominated convergence in Frechet spaces, by the way yielding more detailed information on the structure of the underlying spaces. On the other hand, Baire's approach is an easy tool to develop condensation principles by considering residual sets. Finally, some typical applications concerning trigonometric Fourier partial sums may illustrate the result received. 相似文献
66.
Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, and f(x1,…, xn) be a multilinear polynomial over C, which is not central valued on R. Suppose that F and G are two generalized derivations of R and d is a nonzero derivation of R such that d(F(f(r))f(r) ? f(r)G(f(r))) = 0 for all r = (r1,…, rn) ∈ Rn, then one of the following holds:
There exist a, p, q, c ∈ U and λ ∈C such that F(x) = ax + xp + λx, G(x) = px + xq and d(x) = [c, x] for all x ∈ R, with [c, a ? q] = 0 and f(x1,…, xn)2 is central valued on R;
There exists a ∈ U such that F(x) = xa and G(x) = ax for all x ∈ R;
There exist a, b, c ∈ U and λ ∈C such that F(x) = λx + xa ? bx, G(x) = ax + xb and d(x) = [c, x] for all x ∈ R, with b + αc ∈ C for some α ∈C;
R satisfies s4 and there exist a, b ∈ U and λ ∈C such that F(x) = λx + xa ? bx and G(x) = ax + xb for all x ∈ R;
There exist a′, b, c ∈ U and δ a derivation of R such that F(x) = a′x + xb ? δ(x), G(x) = bx + δ(x) and d(x) = [c, x] for all x ∈ R, with [c, a′] = 0 and f(x1,…, xn)2 is central valued on R.
67.
V. V. Bavula 《代数通讯》2013,41(8):3219-3261
The left quotient ring (i.e., the left classical ring of fractions) Qcl(R) of a ring R does not always exist and still, in general, there is no good understanding of the reason why this happens. In this article, existence of the largest left quotient ring Ql(R) of an arbitrary ring R is proved, i.e., Ql(R) = S0(R)?1R where S0(R) is the largest left regular denominator set of R. It is proved that Ql(Ql(R)) = Ql(R); the ring Ql(R) is semisimple iff Qcl(R) exists and is semisimple; moreover, if the ring Ql(R) is left Artinian, then Qcl(R) exists and Ql(R) = Qcl(R). The group of units Ql(R)* of Ql(R) is equal to the set {s?1t | s, t ∈ S0(R)} and S0(R) = R ∩ Ql(R)*. If there exists a finitely generated flat left R-module which is not projective, then Ql(R) is not a semisimple ring. We extend slightly Ore's method of localization to localizable left Ore sets, give a criterion of when a left Ore set is localizable, and prove that all left and right Ore sets of an arbitrary ring are localizable (not just denominator sets as in Ore's method of localization). Applications are given for certain classes of rings (semiprime Goldie rings, Noetherian commutative rings, the algebra of polynomial integro-differential operators). 相似文献
68.
Given a digraph G, we propose a new method to find the recurrence equation for the number of vertices of the k‐iterated line digraph , for , where . We obtain this result by using the minimal polynomial of a quotient digraph of G. 相似文献
69.
70.
本文讨论了周期结构复合材料特征值的多尺度计算,提出了高阶多尺度Rayleigh商校正算法,并给出了收敛性分析. 最后,通过大量数值实验结果表明,新算法是有效且必要的. 相似文献