共查询到20条相似文献,搜索用时 31 毫秒
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We introduce and study equational domains and equational codomains. Informally, an equational domain is an algebra every finite
union of algebraic sets over which is an algebraic set; an equational codomain is an algebra every proper finite union of
algebraic sets over which is not an algebraic set. 相似文献
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A well-known theorem due to E. Zelmanov proves that PI-Lie algebras with an algebraic adjoint representation over a field of characteristic zero are locally finite-dimensional. In particular, a Lie algebra (over a field of characteristic zero) whose adjoint representation is algebraic of bounded degree is locally finite-dimensional. In this paper it is proved that a prime nondegenerate PI-Lie algebra with an algebraic adjoint representation over a field of characteristic zero is simple and finite-dimensional over its centroid, which is an algebraic field extension of the base field. We also give a new and shorter proof of the local finiteness of Lie algebras with an algebraic adjoint representation of bounded degree. 相似文献
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In this paper, we characterize the set of all binary algebraic (or polynomial) operations of an idempotent algebra that has at least one r-ary algebraic operation, (r ≥ 2), depending on every variable such that there is no an (r+2)-ary algebraic operation depending on at least (r+1) variables. We prove that this set forms a finite Boolean algebra, and then we characterize this Boolean algebra. 相似文献
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Marko Kandić 《Linear and Multilinear Algebra》2016,64(6):1185-1196
In this paper, we find sufficient and necessary conditions for a triangularizable closed algebra of polynomially compact operators to be commutative modulo the radical. We also prove that an algebraic algebra of operators of a bounded degree on a Banach space is triangularizable under some mild additional conditions. As a special case we obtain a result stating that every algebraic algebra of operators of bounded degree is triangularizable whenever its commutators are nilpotent operators. 相似文献
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Let (U; F) be an idempotent algebra. There is an r-ary essentially algebraic operation in F where there is not any (r + 3)-ary algebraic operation depending on at least r + 1 variables. In this paper, we prove that the set of all 4-ary algebraic operations of this algebras forms a finite De Morgan algebra, and then we characterize this De Morgan algebra. 相似文献
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HEYTING代数与FUZZY蕴涵代数 总被引:5,自引:0,他引:5
Heyting代数是作为直觉主义命题逻辑的代数模型而引进的Fuzzy蕴涵代数是 [0 ,1]值逻辑的蕴函联结词的一种代数抽象 .本文给出Heyting代数的若干基本性质 ,并证明了Heyting代数是Fuzzy蕴涵代数 ,也是Heyting型Fuzzy蕴涵代数。 相似文献
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WANG Dengyin Department of Mathematics China University of Mining Technology Xuzhou China 《中国科学A辑(英文版)》2005,48(6):808-818
With one exception, the holomorph of a finite dimensional abelian connected algebraic group is shown to be a complete generalized algebraic group. This result on algebraic group is an analogy to that on Lie algebra. 相似文献
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A. Ensor 《Algebra Universalis》1997,38(1):1-14
The idea of an algebra in is introduced. Within congruence modular varieties such algebras are shown to be the abelian algebras with a one-element
subalgebra. This leads on to the notion of algebraic coalition, which is characterized for congruence modular varieties and
for varieties of Jónsson–Tarski algebras. This characterization displays an intimate relationship between algebraic coalitions,
Gumm difference terms, and the centre of an algebra.
Received July 16, 1996; accepted in final form May 2, 1997. 相似文献
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We study algebraic properties of the Wiener algebra of absolutely convergent power series on the closed unit disc. In particular, we prove a form of Weierstrass preparation for algebraic functions in this algebra. 相似文献
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Antoine Touzé 《Advances in Mathematics》2010,225(1):33-68
We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study of classical algebraic groups, such as a cohomological stabilization property, the injectivity of external cup products, and the existence of Hopf algebra structures on the (stable) cohomology of a classical algebraic group with coefficients in a Hopf algebra. Our result also opens the way to new explicit cohomology computations. We give an example inspired by recent computations of Djament and Vespa. 相似文献
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J.A. Loustau 《代数通讯》2013,41(12):2507-2522
The Arens construction of dii algebra in the biduai bpcice of an algebra has provided in functional analysis a useful method for constructing an algebra containing a rich supply of idempotcnts As idera-potents are an Important too] in the study of non-associative algebras, we begin in this paper the study of the algebraic biduai of a nonassociative algebra. In particular, we obtain a partial spectral decomposition for a transcendental element of a power associative algebra by analyzing the biduai of the associative subaigebra it generates. 相似文献
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Lattice implication algebra is an algebraic structure that is established by combining lattice and implicative algebra. It originated from the study on lattice-valued logic. In this paper, we characterize two special classes of lattice implication algebra, namely, subdi-rectly irreducible and directly indecomposable lattice implication algebras. Some important results are obtained. 相似文献
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Alessandro D'Andrea 《Journal of Algebra》2008,319(5):2106-2112
I give a short proof of the following algebraic statement: in a simple vertex algebra, the underlying Lie conformal algebra is either abelian, or it is an irreducible central extension of a simple Lie conformal algebra. This provides many examples of non-finite simple Lie conformal algebras, and should prove useful for classification purposes. 相似文献
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《Quaestiones Mathematicae》2013,36(2):93-100
Opgedra aan Prof. Hennie Schutte by geleentheid van sy sestigste verjaarsdag. Abstract A Boolean algebra is the algebraic version of a field of sets. The complex algebra C(B) of a Boolean algebra B is defined over the power set of B; it is a field of sets with extra operations. The notion of a second-order Boolean algebra is intended to be the algebraic version of the complex algebra of a Boolean algebra. To this end a representation theorem is proved. 相似文献
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A. V. Antonov 《Theoretical and Mathematical Physics》1997,113(3):1520-1529
We prove that an integrable system solved by the quantum inverse scattering method can be described by a purely algebraic
object (universal R-matrix) and a proper algebraic representation. For the quantum Volterra model, we construct the L-operator
and the fundamental R-matrix from the universal R-matrix for the quantum affine algebra Uq(ŝl2) and the q-oscillator representation for it. Thus, there is an equivalence between an integrable system with the symmetry
algebra A and the representation of this algebra.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 3, pp. 384–396, December, 1997. 相似文献
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In Tang and Bai [Math Nachr. 2012;285:922–935] classified a class of non-graded left-symmetric algebraic structures on the Witt algebra under a certain rational condition. In this note, we show that this rational condition is not necessary. This leads to a more elegant classification of the left-symmetric algebraic structures and Novikov algebraic structures on the Witt algebra. 相似文献
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Catriona Maclean 《Mathematische Nachrichten》2019,292(1):121-126
In 2 , Huayi Chen introduces the notion of an approximable graded algebra, which he uses to prove a Fujita‐type theorem in the arithmetic setting, and asks if any such algebra is a sub‐algebra of the graded section ring of a big line bundle on an algebraic variety. We give a counter‐example showing that this is not the case. 相似文献
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Bienvenido Cuartero José E. Galé Arkadii M. Slinko 《Proceedings of the American Mathematical Society》1997,125(7):1945-1952
It is proved that if the dual Lie algebra of a Lie coalgebra is algebraic, then it is algebraic of bounded degree. This result is an analog of the D.Radford's result for associative coalgebras.