共查询到20条相似文献,搜索用时 15 毫秒
1.
Hai-Yang Li Sheng-Gang Li 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2008,12(5):487-492
This paper is devoted to congruences and ideals in pseudoeffect algebras. Let I be a normal ideal in a pseudoeffect algebra E. We show that: (1) the relation ~
I
induced by I is a congruence if and only if for every a∈E, I∩ [0,a] is upper directed; (2) the relation ~
I
induced by I is a strong congruence if and only if I is a normal weak Riesz ideal in a pseudoeffect algebra E. Moreover, we introduce a stronger concept of congruence—namely Riesz strong congruence—and we prove that, if I is a normal weak Riesz ideal in a pseudoeffect algebra E, then ~
I
is a Riesz strong congruence and, conversely, if ~ is a Riesz strong congruence, then I = [0]~ is a normal weak Riesz ideal, and ~
I
= ~.
This work was supported by the National Natural Science Foundation of China (Grant No. 10271069). 相似文献
2.
Yongjian Xie Yongming Li 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2010,14(4):387-398
We prove that there is an order isomorphism between the lattice of all normal Riesz ideals and the lattice of all Riesz congruences
in upwards directed generalized pseudoeffect algebras (or GPEAs, for short). We give a sufficient and necessary condition
under which a normal Riesz ideal I of a weak commutative generalized pseudoeffect algebra P is a normal Riesz ideal also in the unitization [^(P)]\widehat{P} of P. These results extend those obtained recently by Avalllone, Vitolo, Pulmannová and Vinceková for effect algebras. At the
same time, we give the conditions under which the quotient of a generalized pseudoeffect algebra P is a generalized effect algebra and linearly ordered generalized pseudoeffect algebra. 相似文献
3.
Gejza Jenča 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2013,17(1):45-47
We prove that for every lattice effect algebra, the system of all congruences generated by the prime ideals of the compatibility center separates the elements. This is a common generalization of Chang’s representation theorem from 1959 and a result of Graves and Selesnick (Colloq Math 27:21–30, 1973). 相似文献
4.
ZhiHao Ma 《Information Sciences》2009,179(5):505-2486
We show that in a lattice effect algebra, each lattice ideal is an effect algebra ideal if and only if the lattice effect algebra is an orthomodular lattice. 相似文献
5.
Anatolij Dvure?enskij 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2011,15(9):1825-1833
Recently, in Dvurečenskij (, 2011), it was shown that if a pseudo effect algebra satisfies a kind of the Riesz decomposition property (RDP), then its state
space is either empty or a nonempty simplex. This will allow us to prove a Yosida–Hewitt type and a Lebesgue type decomposition
for measures on pseudo effect algebra with RDP. The simplex structure of the state space will entail not only the existence
of such a decomposition but also its uniqueness. 相似文献
6.
7.
Yun Shang Ruqian Lu 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2007,11(9):847-853
In this paper, we describe the relationships between pseudo MV algebras and semirings. We also give definitions of automata
on lattice ordered semirings, prove that the family of K-Languages is closed under union, and discuss the conditions for the closedness of families of K-languages under intersection, generalized intersection and reversal operations. 相似文献
8.
Molodtsov引入的软集理论,可作为通用的数学工具去处理不确定性问题。给出了BCI代数上的反模糊软理想的概念,对它们的并、交和AND的性质进行了研究,定义了BCI代数上的模糊软理想间的模糊软同态和模糊软同构,给出了BCI代数上的模糊软理想的同构像定理和同态逆像定理。 相似文献
9.
Rzvan Diaconescu 《Information Processing Letters》2009,109(23-24):1245-1251
We introduce a semantic encoding of partial algebras as total algebras through a Horn axiomatization of the existence equality relation interpreted as an algebraic operation. We show that this novel encoding enjoys several important properties that make it a good tool for the execution of partial algebraic specifications through means specific to ordinary algebraic reasoning, such as term rewriting. 相似文献
10.
引入BR0代数的Fuzzy理想与素Fuzzy理想的概念;给出了Fuzzy理想与素Fuzzy理想的等价形式;在(素)Fuzzy理想基础之上又进一步引入了(素)直觉Fuzzy理想,并通过Fuzzy理想找到了它们与(素)理想之间的关系。 相似文献
11.
介绍了伪MTL代数的一些重要性质,引入了伪MTL代数的滤子、素滤子以及极大滤子的概念,研究了它们的性质以及它们之间的关系。 相似文献
12.
13.
Anatolij Dvurečenskij Miroslav Kolařík 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2014,18(6):1041-1053
We study the Riesz decomposition property types of the lexicographic product of two po-groups. Then we apply them to the study of pseudo effect algebras which can be decomposed into a comparable system of non-void slices indexed by some subgroup of real numbers. Finally, we present their representation by the lexicographic product. 相似文献
14.
王丰效 《计算机工程与应用》2018,54(9):54-56
模糊子代数是模糊代数的一个重要研究内容。为了进一步了解坡代数的模糊理想的特性,在坡代数中引入了区间值模糊理想概念。讨论了坡代数的区间值模糊理想的相关性质。证明了坡代数的区间值模糊理想的交,直积以及同态像也是区间值模糊理想。 相似文献
15.
BR0代数的模糊理想与直觉模糊理想 总被引:1,自引:0,他引:1
引入BR0代数的Fuzzy理想与素Fuzzy理想的概念;给出了Fuzzy理想与素Fuzzy理想的等价形式;在(素)Fuzzy理想基础之上又进一步引入了(素)直觉Fuzzy理想,并通过Fuzzy理想找到了它们与(素)理想之间的关系。 相似文献
16.
Fuzzy maximal ideals of BCI and MV algebras 总被引:1,自引:0,他引:1
C. S. Hoo
S. Sessa
《Information Sciences》1994,80(3-4):299-309We consider fuzzy maximal ideals of BCI, BCK, and MV algebras, and show that such fuzzy ideals take only the values {0,1}, and have level ideals which are maximal ideals of the algebra. It is shown that fuzzy maximal ideals of commutative BCK algebras are fuzzy prime. We establish a correspondence between ideals and fuzzy ideals. In a bounded BCK algebra, this correspondence is one-to-one between maximal ideals and fuzzy maximal ideals. We also show how to construct fuzzy ideals which are not characteristic functions of ideals of an MV algebra. 相似文献
17.
《国际计算机数学杂志》2012,89(10):1388-1411
In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals of finite-dimensional Lie algebras, starting from the non-zero brackets in its law. In order to implement this method, we use the symbolic computation package MAPLE 12. Moreover, we also give a brief computational study considering both the computing time and the memory used in the two main routines of the implementation. Finally, we determine the maximal dimension of abelian subalgebras and ideals for non-decomposable solvable non-nilpotent Lie algebras of dimension 6 over both the fields ? and ?, showing the differences between these fields. 相似文献
18.
彭家寅 《计算机工程与应用》2018,54(11):62-66
将犹豫模糊集应用于[BR0]代数的滤子和理想理论中,初步建立[BR0]代数的犹豫模糊滤子与理想理论。引入了[BR0]代数的犹豫模糊滤子、犹豫模糊理想和犹豫模糊素理想的概念,研究它们的基本性质,给出了[BR0]代数的犹豫模糊集成为犹豫模糊滤子(犹豫模糊理想)的条件,证明了[BR0]代数的犹豫模糊滤子、犹豫模糊理想和犹豫模糊素理想关于交运算具有封闭性,指出了犹豫模糊滤子、犹豫模糊理想和犹豫模糊素理想在[BR0]代数同构下的不变性。 相似文献
19.
在格蕴涵代数中,证明了极小素理想与极小格素理想的等价性,继而给出了极小素理想与零化子的相互表示定理。提出了格蕴涵代数中的[α]-理想概念并给出其若干等价刻画,证明了极小素理想是[α]-理想。证明了全体素[α]-理想之集[Sα(L)]是一个紧的Stone空间,进一步给出[Sα(L)]分别是[T1、][T2]拓扑空间的充要条件。 相似文献
20.
T. Vetterlein 《Information Sciences》2010,180(24):5101-5114
It is well-known that the representation of several classes of residuated lattices involves lattice-ordered groups. An often applicable method to determine the representing group (or groups) from a residuated lattice is based on partial algebras: the monoidal operation is restricted to those pairs that fulfil a certain extremality condition, and else left undefined. The subsequent construction applied to the partial algebra is easy, transparent, and leads directly to the structure needed for representation.In this paper, we consider subreducts of residuated lattices, the monoidal and the meet operation being dropped: the resulting algebras are pseudo-BCK semilattices. Assuming divisibility, we can pass on to partial algebras also in this case. To reconstruct the underlying group structure from this partial algebra, if applicable, is again straightforward. We demonstrate the elegance of this method for two classes of pseudo-BCK semilattices: semilinear divisible pseudo-BCK algebras and cone algebras. 相似文献