平衡双重半拟补MS代数的理想和同余关系

在平衡双重半拟补MS代数上引入(*)理想,(+)理想,(°)理想和(*,+,°)理想的概念,探讨平衡双重半拟补MS代数上(*)理想,(+)理想,(°)理想和(*,+,°)理想与核理想的关系,获得了(°)理想是核理想的结论.同时构造出了以(*,+,°)理想为核的最小同余关系和最大同余关系,并获得了最小同余关系和最大同余关...     

分配P-代数的核理想与余核滤子

本文的主要结果是给出了分配P-代数中一个理想成为核理想的充要条件,同时提出了余核滤子的概念,研究了核理想与余核滤子之间的某些内在联系.     

关于Robbins代数与Heyting代数的类似性质

Ｓ．Ｗｉｎｋｅｒ在文〔１〕中给出了Ｒｏｂｂｉｎｓ代数成为Ｂｏｏｌｅａｎ代数的一个较弱的条件。本文将讨论Ｈｅｙｔｉｎｇ代数成为Ｂｏｏｌｅａｎ代数的条件，我们发现Ｈｅｙｉｎｇ代数成为Ｂｏｏｌｅａｎ代数的条件与Ｒｏｂｂｉｎｓ代数成为Ｂｏｏｌｅａｎ代数的条件相似，从而提示了Ｈｅｙｔｉｎｇ代数与Ｒｏｂｂｉｎｓ代数之间具有一定的关系。     

BCK-代数的模糊代数理想

在有界可换BCK-代数上引入了Fuzzy代数理想的概念,给出了Fuzzy代数理想的某些特征,讨论了Fuzzy理想与Fuzzy代数理想的关系。最后描述了全体Fuzzy集的BCK-代数特征。     

BCH-代数的模糊理想与模糊H-理想

在BCK／BCI／BCC代数中Fuzzy理想被广泛研究，但在BCH-代数中还没有讨论过。在BCH-代数中引人了Fuzzy理想与FuzzyH-理想的概念，并讨论它们的性质。     

BCK-代数的极小理想与次极小理想

在BCK-代数中,引入了极小理想与次极小理想的概念,研究了极小与次极小理想的若干性质,它们同文[5]、文[6]中的有关概念与结果是对偶的.     

BCK-代数的L-fuzzy理想

给出 BCK-代数的 L- fuzzy子代数和 L- fuzzy理想等概念的等价刻画。     

BCI-代数的余模糊理想

在BCI-代数中引入了余模糊理想的概念,讨论了它的某些性质,研究了BCI-代数的模糊理想和余模糊理想的关系.特别是,给出了一个如何由一个模糊子集生成一个余模糊理想和闭余模糊理想的过程.     

有界Heyting代数的交换理想与关联理想

运用泛代数和格理论的方法和原理进一步深入研究有界Heyting代数的理想问题。在有界Heyting代数中引入了交换理想、关联理想和正关联理想概念并讨论了它们的性质和相互关系。获得了各种理想的若干等价刻画。证明了在有界Heyting代数中,关联理想和正关联理想等价;在Ockham型有界Heyting代数中,理想和交换理想等价。同时,给出了有界Heyting代数的交换理想成为关联理想的一个充分必要条件。     

因子中原子CSL代数的Lie理想

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．     

Diagonal invariant ideals of Toeplitz algebras on discrete groups

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.     

双重伪补代数的假值理想的一点注记

介绍了双重伪补代数的假值理想和假值同余的概念,并刻画了它们的某些性质.特别地,给出了双重伪补代数的假值理想和假值同余的特征表示.     

Normalization of monomial ideals and Hilbert functions

We study the normalization of a monomial ideal, and show how to compute its Hilbert function (using Ehrhart polynomials) if the ideal is zero dimensional. A positive lower bound for the second coefficient of the Hilbert polynomial is shown.

     

Some Boolean algebras with finitely many distinguished ideals II

We describe the countably saturated models and prime models (up to isomorphism) of the theory Th_prin of Boolean algebras with a principal ideal, the theory Th_max of Boolean algebras with a maximal ideal, the theory Th_ac of atomic Boolean algebras with an ideal such that the supremum of the ideal exists, and the theory Th_sa 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 T_X of Boolean algebras with distinguished ideals to be elementarily equivalent to a countably saturated model of T_X.     

Modules and ideals of algebras of associative type

In this paper, we study some properties of algebras of associative type introduced in previous papers of the author. We show that a finite-dimensional algebra of associative type over a field of zero characteristic is homogeneously semisimple if and only if a certain form defined by the trace form is nonsingular. For a subclass of algebras of associative type, it is proved that any module over a semisimple algebra is completely reducible. We also prove that any left homogeneous ideal of a semisimple algebra of associative type is generated by a homogeneous idempotent.     

Oriented tree diagram Lie algebras and their abelian ideals

We introduce oriented tree diagram Lie algebras which are generalized from Xu＇s both upward and downward tree diagram Lie algebras, and study certain numerical invariants of these algebras related to abelian ideals.     

Hyper MV ‐ideals in hyper MV ‐algebras

In this paper we define the hyper operations ?, ∨ and ∧ on a hyper MV ‐algebra and we obtain some related results. After that by considering the notions ofhyper MV ‐ideals and weak hyper MV ‐ideals, we prove some theorems. Then we determine relationships between (weak) hyper MV ‐ideals in a hyper MV ‐algebra (M, ⊕, *, 0) and (weak) hyper K ‐ideals in a hyper K ‐algebra (M, °, 0). Finally we give a characterization of hyper MV ‐algebras of order 3 or 4 based on the (weak) hyper MV ‐ideals (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Best bounds for approximate identities in ideals of the Fourier algebra vanishing on subgroups

In this paper we show that if is an amenable locally compact group and if is a closed subgroup, then the ideal has an approximate identity of norm If is not open, this bound is the best possible.

     

On Jordan ideals and submodules: Algebraic and analytic aspects

Let

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be an algebra, and let X be an arbitrary

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-bimodule. A linear space Y ? X is called a Jordan

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-submodule if Ay + yA ∈ Y for all A ∈

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and y ∈ Y. (For X =

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, this coincides with the notion of a Jordan ideal.) We study conditions under which Jordan submodules are subbimodules. General criteria are given in the purely algebraic situation as well as for the case of Banach bimodules over Banach algebras. We also consider symmetrically normed Jordan submodules over C*-algebras. It turns out that there exist C*-algebras in which not all Jordan ideals are ideals.