效应代数成为布尔代数的充要条件

通过效应代数中的中心元引入效应代数中的Well Inside 关系,研究了效应代数中的Well Inside关系的性质;在此基础上得出了效应代数成为布尔代数的一个充要条件。     

分配序列效应代数的理想和同余

分配的序列效应代数（简记为DSEA）,是指在一个效应代数上带有一种乘积运算并满足一定的条件。介绍了分配的序列效应代数中的左理想、右理想、理想、素理想和同余等概念,并且证明了满足（RDP）性质并且以1为乘积单位的分配序列效应代数是具有（RDP）性质的反格分配序列效应代数的子直积。     

序列效应代数的Holland理论

介绍了序列效应代数的概念,给出了交换的序列效应代数的一些性质,证明了交换的序列效应代数由素理想诱导的商代数仍然是交换的序列效应代数。最后证明了每一个交换的序列效应代数能被表示为某个反格的自态射形成的序列效应代数。这样的表示是有用的,因为它给出了一个交换的序列效应代数作为自态射的集合的具体化。     

效应代数水平和上的序列积

建立了一族可和序列效应代数的水平和上具有序列积的充分必要条件,进而给出了由序列效应代数的水平和构造序列效应代数的一种方法。     

由可精确测量元控制的弱可换的伪效应代数

主要研究了由可精确测量元控制的弱可换的伪效应代数中可精确测量元。证明了可精确测量元控制的弱可换的伪效应代数中可精确测量元是弱可换的伪正交代数代数。讨论了弱可换的伪效应代数与BZ-偏序集之间的关系。讨论了弱可换的伪效应代数商代数中可精确测量元与正规Riesz理想之间的关系。     

效应代数的T-模糊滤子

研究了效应代数上的[T-]模糊滤子的一些问题。利用水平截集及范数的方法获得了一些相关的结果,推广了效应代数模糊滤子的一些结果,得到存在一个映射使得效应代数的所有[T-]模糊滤子与这个效应代数的[T-]同余关系对应的结论。     

伪效应代数中的模糊滤子与模糊理想

在伪效应代数中提出了模糊滤子和模糊理想的概念,讨论了它们的性质;引入并研究了强模糊滤子和强模糊理想,得到了一些好的结论。     

粗糙集代数与BR0代数

讨论粗糙集代数与脓。代数的关系,以及由粗糙集代数构造BR0代数的方法。借助近似代数的原子及同余关系,证明了在适当选取蕴涵算子及余运算之后,粗糙集代数就成为BR0代数。     

抽象数据类型的双代数结构及其计算

程序语言中的许多抽象数据类型包含了可递归定义的语法构造和可共递归定义的动态行为特征,因此单纯利用代数或共代数难以给出完整的描述.双代数是同一载体集上的代数和共代数对,提供了一种从范畴论的角度探讨抽象数据类型上的语法构造和动态行为关系及性质的可行途径.给出抽象数据类型的双代数结构,并利用代数函子对共代数函子的分配律描述了语法构造与动态行为之间的自然转换关系;利用分配律对共代数和代数函子进行函子化提升,给出一种构造初始代数(或终结共代数)上的共代数(或代数)结构,并将其提升为初始(或终结)λ-双代数的方法.在此基础上,进一步将函子化提升应用于各种递归(包括迭代和原始递归)及共递归函数(包括共迭代和原始共递归)的定义及计算中,并给出相应的计算定律.     

基于蕴涵算子的粗糙集代数与R0-代数

讨论了粗糙集代数与R0-代数的关系以及由粗糙集代数构造R0-代数的方法。粗糙集本身具有格结构,证明了在适当选取蕴涵算子之后,粗糙集代数就成为R0-代数。     

An ideal topology type convergent theorem on scale effect algebras

The famous Antosik-Mikusinski convergent theorem on the Abel topological groups has very extensive applications in measure theory, summation theory and other analysis fields. In this paper, we establish the theorem on a class of effect algebras equipped with the ideal topology. This paper shows also that the ideal topology of effect algebras is a useful topology in studying the quantum logic the- ory.     

Cartesian product of compressible effect algebras

In the paper, we prove that is compatible with p}, the set of commutant of p, and , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of E _i is a compressible effect algebra if and only if each E _i is a compressible effect algebra. This work was supported by the SF of Education Department of Shaanxi Province (Grant No. 07JK267), P. R. China.     

Generalized Ideals and Supports in Pseudo Effect Algebras

In this paper we introduce the definitions of generalized ideals and generalized filters in pseudo effect algebras. From the generalized ideals (filters), we obtain some equivalent characterization of ideals (filters). The relationships among generalized ideals, ideals and local ideals are studied in detail. We also establish an isomorphism between the set of supports and the set of generalized ideals of pseudo effect algebras.     

On a new class of finite dimensional estimation algebras

We introduce a new class of solvable finite dimensional estimation algebras that contains both the linear and the Bene cases. The condition for finite dimensionality is expressed in terms of two matrices. They play an important role in understanding the structure of estimation algebras.     

The logic of Peirce algebras

Peirce algebras combine sets, relations and various operations linking the two in a unifying setting. This paper offers a modal perspective on Peirce algebras. Using modal logic a characterization of the full Peirce algebras is given, as well as a finite axiomatization of their equational theory that uses so-called unorthodox derivation rules. In addition, the expressive power of Peirce algebras is analyzed through their connection with first-order logic, and the fragment of first-order logic corresponding to Peirce algebras is described in terms of bisimulations.     

Theorems on the structure of finite dimensional estimation algebras

In this paper we proved several theorems concerning the structure of finite dimensional estimation algebras. In particular, under proper technical assumptions, we proved the following: (1) The observation of a filtering system must be linear if the estimation algebra is finite dimensional. (2) All elements of a finite dimensional estimation algebra belong to a special class of polynomial differential operators. (3) All finite dimensional estimation algebras are solvable.     

An algorithmic approach to resolutions

We provide an algorithmic method for constructing projective resolutions of modules over quotients of path algebras. This algorithm is modified to construct minimal projective resolutions of linear modules over Koszul algebras.     

On pseudo-BL algebras and BCC-algebras

We further study the filter theory of pseudo-BL algebras. We give some equivalent conditions of filter, normal filter and Boolean filter. We introduce the notion of pseudo MV-filter, pseudo-G filter and characterize Boolean algebras, pseudo-MV algebras and pseudo Gödel algebras (i.e. Gödel algebras) in pseudo-BL algebras. We establish the connections between BCC-algebras, pseudo-BCK algebras, pseudo-BL algebras and weak pseudo-BL algebras (pseudo-MTL algebras).     

Weak pseudo-Wajsberg and weak pseudo-MV algebras

 We introduce and study a generalization of pseudo-Wajsberg and pseudo-MV algebras. The weakening of the axioms leads to the existence of two lattice structures, and of two multiplicative monoid structures. Some categorical equivalences are established.     

Some new simple Lie algebras in characteristic 2

We describe an algorithm for computing automorphism groups and testing isomorphisms of finite dimensional Lie algebras over finite fields. The algorithm is particularly effective for simple or almost simple Lie algebras. We show how it can be used in a computer search for new low dimensional simple Lie algebras over the field with two elements.