共查询到20条相似文献,搜索用时 31 毫秒
1.
V. T. Filippov 《Algebra and Logic》1996,35(2):120-128
Let Φ be an associative commutative ring with unity, 1/6 ∈ Φ, write A for a Mal’tsev algebra over Φ, suppose that on A, the
function h(y, z, t, x, x)=2[{yz, t, x}x+{yx, z, x}t], where {x, y, z}=(xy)z−(xz)y+2x(yz), is defined, and assume that H(A)
is a fully invariant ideal of A generated by the function h. The algebra A satisfying an identity h(y, z, x, x, x)=0 [h(y,
z, t, x, x)=0] is called a Mal’tsev h0-algebra (h-algebra). We prove that in any Mal’tsev h0-algebra, the inclusion H(A)·A2⊆Ann A holds withAnnA the annihilator of A. This means that any semiprime h0-algebra A is an h-algebra. Every prime h0-algebra A is a central simple algebra over the quotient field Λ of the center of its algebra of right multiplications, R(A),
and is either a 7-dimensional non-Lie algebra or a 3-dimensional Lie algebra over Λ.
Supported by RFFR grant No. 94-01-00381-a.
Translated fromAlgebra i Logika, Vol. 35, No. 2, pp. 214–227, March–April, 1996. 相似文献
2.
Ivan P. Shestakov 《Geometriae Dedicata》1999,77(2):215-223
An Akivis algebra is a vector space V endowed with a skew-symmetric bilinear product [x,y] and a trilinear product A(x,y,z) that satisfy the identity
These algebras were introduced in 1976 by M.A. Akivis as local algebras of three-webs. For any (nonassociative) algebra B one may obtain an Akivis algebra Ak (B) by considering in B the usual commutator [x,y] = xy – yx and associator A(x,y,z) = (xy)z – x(yz). Akivis posed the problem whether every Akivis algebra is isomorphic to a subalgebra of Ak (B) for a certain B. We prove that this problem has a positive answer. 相似文献
3.
本文用 Siegel-Tatuzawa定理证明了:当n>1.2×10~11时,至多有两个正 整数n。使方程xu+yz+zx=n无适合(x,y,z)=1且0<x<y<z的解(x,y,z), 并给出类数为2的二次域与多项式表素数的一个结果. 相似文献
4.
V. T. Filippov 《Algebra and Logic》1997,36(1):60-71
Let A be a free alternative Φ-algebra, where Φ is an associative commutative ring with 1, containing 1/6, and g(y, z, t, v,
x, x)=2[J_({[y, z], t, x}_, x, v)+J_({[y,x], z, x}_, t, v)], where [x, y]=xy−yx, J_(x, y, z)=[[x, y], z]+[[z, x], y]+[[y,
z], x], {x, y, z}_=J_(x, y, z)+3[x, [y, z]]. We construct trivial nuclear ideals of A, that is, nonzero ideals with zero multiplication,
lying in the associative center of A. In particular, it is shown that if G and B are fully invariant ideals of A on k≥7 free
generators, generated by a function g and by double commutators, respectively, then GB+BG is a nuclear ideal of A. This implies
that an unmized alternative algebra satisfies GB=BG=0. If an unmixed algebra is finitely generated, then G=0. In addition,
we prove that if R is an unmixed solvable alternative algebra then (RN)2=0 for some N.
Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 97–115, January–February, 1997. 相似文献
5.
关于方程xy+yz+zx=n的正整数解 总被引:1,自引:1,他引:0
本文在广义Riemann猜想成立的条件下证明了:当且仅当正整数n=1,2,4,6,10,18,22,30,42,58,70,78,102,130,190,210,330,462时,方程xy+yz+zx=n无正整数解(x,y,z). 相似文献
6.
Bronislaw Wajnryb 《Israel Journal of Mathematics》1982,43(2):169-176
LetR be a Krull subring of a ring of polynomialsk[x
1, …, xn] over a fieldk. We prove that ifR is generated by monomials overk thenr is affine. We also construct an example of a non-affine Krull ringR, such thatk[x, xy]⊂R⊂k[x, y], and a non-Noetherian Krull ringS, such thatk[x, xy, z]⊂S⊂k[x, y, z]. 相似文献
7.
Let (G, ·) be a group, (H, +) be an abelian group, and ${f:G\rightarrow H}$ . The second order Cauchy difference of f is $$C^{(2)}f(x,y,z)=f(xyz)-f(xy)-f(yz)-f(xz)+f(x)+f(y)+f(z).$$ The functional equation $$C^{(2)}f(x,y,z)=0$$ is studied. We present its general solution on free groups. Solutions on other selected groups are also given. 相似文献
8.
V. T. Filippov 《Algebra and Logic》1997,36(3):193-203
Let ϕ be an associative commutative ring with 1, containing 1/6, and A be an alternative ϕ-algebra. Let D be an associator
ideal of A and H a fully invariant ideal of A, generated by all elements of the form h(y, z, t, x, x)=[{[y, z], t, x}-, x]+[{[y,
x], z, x}-, t], where [x, y]=xy−yx, {x, y, z}-=[[x, y], z]−[[x, z], y]+2[x,[y, z]]. Here we consider an ideal Q=H∩D and prove
that Q4=0 in the algebra A. If A is unmixed, then HD=0, DH=0, and Q2=0 in particular. If A is a finitely generated unmixed algebra, then the ideal H lies in its associative center and Q=0. It
follows that any finitely generated purely alternative algebra satisfies the identity h(y,z,t,x,x)=0. We also show that a
fully invariant ideal H0 of the unmixed algebra A, generated by all elements of the form h(x, z, t, x, x), lies in its associative center and H0∩D=0. Consequently, every purely alternative algebra satisfies the identity h(x,z,t,x,x)=0.
Translated fromAlgebra i Logika, Vol. 36, No. 3, pp. 323–340, May–June, 1997. 相似文献
9.
The classification of extended affine Lie algebras of type A_1 depends on the Tits-Kantor- Koecher (TKK) algebras constructed from semilattices of Euclidean spaces.One can define a unitary Jordan algebra J(S) from a semilattice S of R~v (v≥1),and then construct an extended affine Lie algebra of type A_1 from the TKK algebra T(J(S)) which is obtained from the Jordan algebra J(S) by the so-called Tits-Kantor-Koecher construction.In R~2 there are only two non-similar semilattices S and S′,where S is a lattice and S′is a non-lattice semilattice.In this paper we study the Z~2-graded automorphisms of the TKK algebra T(J(S)). 相似文献
10.
Patrick Dehornoy 《代数通讯》2013,41(6):1967-1978
We prove a result conjectured by J.Je[zcirc]ek in [9],namely that a zeropotent left self-distributive system need not be 3-trivial, i.e.,the identity x(yz)=0 does not follow from the identities x(yz)=(xy)(xz),xx=0 and x0=0x=0.The argument is a general scheme possibly working for various identities in the context of self-distributivity. 相似文献
11.
We obtain exact solutions U(x, y, z, t) of the three-dimensional sine-Gordon equation in a form that Lamb previously proposed
for integrating the two-dimensional sine-Gordon equation. The three-dimensional solutions depend on arbitrary functions F(α)
and ϕ(α,β), whose arguments are some functions α(x, y, z, t) and β(x, y, z, t). The ansatzes must satisfy certain equations. These
are an algebraic system of equations in the case of one ansatz. In the case of two ansatzes, the system of algebraic equations
is supplemented by first-order ordinary differential equations. The resulting solutions U(x, y, z, t) have an important property,
namely, the superposition principle holds for the function tan(U/4). The suggested approach can be used to solve the generalized sine-Gordon equation, which, in contrast to the classical equation,
additionally involves first-order partial derivatives with respect to the variables x, y, z, and t, and also to integrate
the sinh-Gordon equation. This approach admits a natural generalization to the case of integration of the abovementioned types
of equations in a space with any number of dimensions.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 370–377, March, 2009. 相似文献
12.
Let (S, #, *) be an algebraic structure where # and * are binary operations with identities on the set S. Let (G, +) be an abelian group. We consider the functional equation (i) $$f(x * t, y)+ g(x, y\ \sharp\ t) = h(x, y)\ {\rm for\ all}\ x, y, t \in S,$$ where ?,g,h :S × S → G. As an application of (i) we solve $$f(x + t, y)- f(x, y) = -b(f(x, y+t)- f(x,y))\ {\rm for\ all}\ x, y, t \in S,$$ where ? :S × S → K (a field), and b ∈ K is a constant and b ≠ 0, ±1. If b = i, the pure imaginary unit, S = R and K = C, then the above equation may be considered as a discrete analogue of the Cauchy-Riemann equations. When (R, +, ?) is a commutative ring with 1, the functional equation (ii) $$\phi(y+xt)-\phi(xy+xt)=\phi(y+x)-\phi(xy+x)$$ for all x,y,t ∈ R, where ? : R → G, is basic to the general solutions of (i). We solve (ii) on certain rings and fields. 相似文献
13.
Fang LI Gong Xiang LIU 《数学学报(英文版)》2006,22(4):1027-1046
There are at least two kinds of generalization of Hopf algebra, i.e. pre-Hopf algebra and weak Hopf algebra. Correspondingly, we have two kinds of generalized bialgebras, almost bialgebra and weak bialgebra. Let L = (L, ×, I, a, l, r) be a tensor category. By giving up I, l, r and keeping ×, a in L, the first author got so-called pre-tensor category L = (L, ×, a) and used it to characterize almost bialgebra and pre-Hopf algebra in Comm. in Algebra, 32(2): 397-441 (2004). Our aim in this paper is to generalize tensor category L = (L, ×, I, a, l, r) by weakening the natural isomorphisms l, r, i.e. exchanging the natural isomorphism ll^-1 = rr^-1 = id into regular natural transformations lll= l, rrr = r with some other conditions and get so-called weak tensor category so as to characterize weak bialgebra and weak Hopf algebra. The relations between these generalized (bialgebras) Hopf algebras and two kinds generalized tensor categories will be described by using of diagrams. Moreover, some related concepts and properties about weak tensor category will be discussed. 相似文献
14.
Every extended affine Lie algebra of type A
1 and nullity ν with extended affine root system R(A
1, S), where S is a semilattice in ℝ
ν
, can be constructed from a TKK Lie algebra T (J (S)) which is obtained from the Jordan algebra J (S) by the so-called Tits-Kantor-Koecher construction. In this article we consider the ℤ
n
-graded automorphism group of the TKK Lie algebra T (J (S)), where S is the “smallest” semilattice in Euclidean space ℝ
n
. 相似文献
15.
L. Makar-Limanov 《Israel Journal of Mathematics》1990,69(2):250-256
In this note we describe the group of automorphisms of a commutative algebra with three generatorsx, y andz satisfying a relationxy= P(z), whereP(z) is a polynomial.
The author was visiting Bar-Ilan and Tel-Aviv Universities while working on this project. He is deeply thankful for hospitality
rendered. 相似文献
16.
Ludvik Janos 《Annali di Matematica Pura ed Applicata》1977,112(1):273-283
Summary We consider the boundary value problem αz″(x)+m(x)y(x)=0, αy″(x)+p(x)z(x)=0, xε[0, 1], y(0)=y(1)=z(0)=0, where the functions m(x) and p(x) are assumed integrable and positive everywhere in [0, 1]. As the main result we obtain the inequalities
for n=1, 2, ... where δn(m, p) stands for the product
of the first n eigenvalues αi(m, p) of the above system and where δn(m) abbreviates δn(m, m).
Entrata in Redazione il 6 febbraio 1976. 相似文献
17.
A characterization of Lie algebras of skew-symmetric elements of associative algebras with involution is obtained. It is proved that a Lie algebra L is isomorphic to a Lie algebra of skew-symmetric elements of an associative algebra with involution if and only if L admits an additional (Jordan) trilinear operation {x,y,z} that satisfies the identities $$\{x,y,z\}=\{z,y,x\},$$ $$[[x,y],z]=\{x,y,z\}-\{y,x,z\},$$ $$[\{x,y,z\},t]=\{[x,t],y,z\}+\{x,[y,t],z\}+\{x,y,[z,t]\},$$ $$\{\{x,y,z\},t,v\}=\{\{x,t,v\},y,z\}-\{x,\{y,v,t\},z\}+\{x,y,\{z,t,v\}\},$$ where [x,y] stands for the multiplication in L. 相似文献
18.
A Lie module algebra for a Lie algebra L is an algebra and L-module A such that L acts on A by derivations. The depth Lie algebra of a Lie algebra L with Lie module algebra A acts on a corresponding depth Lie module algebra . This determines a depth functor from the category of Lie module algebra pairs to itself. Remarkably, this functor preserves central simplicity. It follows
that the Lie algebras corresponding to faithful central simple Lie module algebra pairs (A,L) with A commutative are simple. Upon iteration at such (A,L), the Lie algebras are simple for all i ∈ ω. In particular, the (i ∈ ω) corresponding to central simple Jordan Lie algops (A,L) are simple Lie algebras.
Presented by Don Passman. 相似文献
19.
Choonkil BAAK 《数学学报(英文版)》2006,22(6):1789-1796
Let X, Y be vector spaces. It is shown that if a mapping f : X → Y satisfies f((x+y)/2+z)+f((x-y)/2+z=f(x)+2f(z),(0.1) f((x+y)/2+z)-f((x-y)/2+z)f(y),(0.2) or 2f((x+y)/2+x)=f(x)+f(y)+2f(z)(0.3)for all x, y, z ∈ X, then the mapping f : X →Y is Cauchy additive.
Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras. 相似文献
20.
一类特殊的Koszul Calabi-Yau DG代数 总被引:1,自引:0,他引:1
假设一个连通上链DG代数A的基分次代数A~#或者同调分次代数H(A)是由一次元素x,y生成的代数kx,y/(xy+yx).本文证明A是Koszul Calabi-Yau DG代数. 相似文献