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孟杰 《纯粹数学与应用数学》1994,10(2):13-18
本文是作者[1]-[6]的继续,我们得到下述结果:定理4.设I是BCK-代数X的一个理想,a是X的一个元素,则包含I和a的最小理想是对某个非负整数}.定理14.设X是一个Lukasiewicz代数,I是X的一个质理想.如果A是X的一个真理想且,则A也是质的.定理15.Lukasiewicz代数X的零理想{0}是质的当且仅当<X;≤>是一个全序集. 相似文献
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环上的典型的线性李代数的理想 总被引:3,自引:0,他引:3
张永正 《纯粹数学与应用数学》1997,13(1):103-108
设R是有1的交换环,本文证明了:当n〉2时,sln(R)的理想都是标准的。当2∈R^*,n〉3时,spn(R)与son(R)的理想也都是标准的。 相似文献
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引进BCI-代数的弱关联理想的概念,并用以刻划弱关联BCI-代数,从而推广了文[3]中的的一上结结论。 相似文献
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给出Quantale代数的概念,得到了单位Quantale是Quantale代数的充要条件,讨论了理想与代数理想的关系,找到了理想不是代数理想的具体例子以及理想是代数理想的充分条件. 相似文献
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Iseki.K.于1975年在BCK-代数中提出了理想和正定理想[1]。我们自1984年以来,对理想作了较深入的研究,分别于1984年和1988年提出了关联理想和可换理想的概念[3],[4]并讨论了各种理想之间的关系。理想在BCK-代数的研究中占有重要的位置。本文利用计算 相似文献
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设B是带有Cartan子代数D的因子,T(L)是B中的原子CLS代数.本文讨论了T(L)中的Lie理想的结构.证明了T(L)中的σ-弱闭子空间L是T(L)的一个Lie理想当且仅当存在T(L)的一个σ-弱闭的结合理想J和T(L)的对角部分的中心的一个子空间E使得(J)~0■L■J E,其中J~0是J中迹为0的元的全体. 相似文献
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Regina Aragn 《Mathematical Logic Quarterly》2003,49(3):260-276
We describe the countably saturated models and prime models (up to isomorphism) of the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal such that the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal such that the supremum of the ideal exists. We prove that there are infinitely many completions of the theory of Boolean algebras with a distinguished ideal that do not have a countably saturated model. Also, we give a sufficient condition for a model of the theory TX of Boolean algebras with distinguished ideals to be elementarily equivalent to a countably saturated model of TX. 相似文献
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P. J. de Paepe 《Czechoslovak Mathematical Journal》2003,53(1):77-81
Examples of non-finitely generated function algebras on planar sets with small maximal ideal spaces are given. 相似文献
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Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero.In this paper we show that any finite-dimensional indecomposable H-module is generated by one element.In particular,any indecomposable submodule of H under the adjoint action is generated by a special element of H.Using this result,we show that the Hopf algebra H is a principal ideal ring,i.e.,any two-sided ideal of H is generated by one element.As an application,we give explicitly the generators of ideals,primitive ideals,maximal ideals and completely prime ideals of the Taft algebras. 相似文献
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This paper is devoted to a general investigation of congruences and ideals in effect algebras. One of our main results is the existence of an order isomorphism between Riesz congruences and Riesz ideals. We also answer an open question of Dvureenskij and Pulmannová by showing that an ideal is a Riesz ideal if and only if it is closed under generalized Sasaki projections. 相似文献
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XU Qingxiang 《数学年刊B辑(英文版)》2000,21(3):367-374
61. IntroductionLet G be a discrete (not necessarily abelian) group. For any subset G of G, we saythat (G, G ) is a quasi-partial ordered group if e 6 G , G ' G G G and G = G ' G ',where e is the unit of G and G ' = {g--' I g e G }; further, (G, G ) is referred to as aquasi-ordered group if G = G u G '. Note that when G7 = G n G ' = {e}, a quasi-partial ordered group (resp. quasi-ordered group) (G, G ) is known as a pajrtially ordered(resp. ordered) group.Let { 6, I g e G } b… 相似文献
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Karla Čipková 《Czechoslovak Mathematical Journal》2006,56(3):933-947
Let A and B be graph algebras. In this paper we present the notion of an ideal in a graph algebra and prove that an ideal extension of
A by B always exists. We describe (up to isomorphism) all such extensions. 相似文献
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整表代数是群代数的推广,它的理想是群代数码的推广.本文给出了整表代数的单边理想是自正交理想的必要充分条件. 相似文献
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许庆祥 《中国科学A辑(英文版)》2002,45(4):462-469
Diagonal invariant ideals of Toeplitz algebras defined on discrete groups are introduced and studied. In terms of isometric
representations of Toeplitz algebras associated with quasi-ordered groups, a character of a discrete group to be amenable
is clarified. It is proved that whenG is Abelian, a closed twosided non-trivial ideal of the Toeplitz algebra defined on a discrete Abelian ordered group is diagonal
invariant if and only if it is invariant in the sense of Adji and Murphy, thus a new proof of their result is given. 相似文献
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关于BCI—代数伴随半群中的可逆元 总被引:4,自引:0,他引:4
给出了BCI-代数的伴随半群中可逆元的刻划,说明BCI-代数的p-半单闭理想与其伴随半群的子群之间有一一对应关系,并证明最大的p-半单闭理想是根理想。 相似文献