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1.
Order - In this paper, we investigate the varieties Mn and Kn of regular pseudocomplemented de Morgan and Kleene algebras of range n, respectively. Priestley duality as it applies to... 相似文献
2.
本文借助弱射影和弱透视的概念刻划了De Morgan代数的同余关系,由此得到了Kalman关于De Morgan代数次直不可约定理的一个新的证明并证明了一个完全分配的De Morgan代数的同余理想与同余关系一一对应的充要条件是L为弱可补的。 相似文献
3.
Hernando Gaitn 《Mathematical Logic Quarterly》1998,44(4):553-567
In this paper we characterize the join irreducible elements of the free algebras on n free generators in the subvarieties of the variety V0 of pseudocomplemented De Morgan algebras satisfying the identity xx′* = (xx′*)′*. 相似文献
4.
Congruence Permutable Symmetric Extended de Morgan Algebras 总被引:1,自引:0,他引:1
Jie FANG 《数学学报(英文版)》2006,22(3):659-664
An algebra A is said to be congruence permutable if any two congruences on it are permutable. This property has been investigated in several varieties of algebras, for example, de Morgan algebras, p-algebras, Kn,0-algebras. In this paper, we study the class of symmetric extended de Morgan algebras that are congruence permutable. In particular we consider the case where A is finite, and show that A is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras. 相似文献
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6.
Congruence relations on de Morgan algebras 总被引:4,自引:0,他引:4
Various classes of de Morgan algebras whose congruence relations satisfy special conditions are investigated together with their interrelationship. In particular, the classes of congruence permutable, congruence regular, and congruence uniform de Morgan algebras are studied.Presented by Joel Berman. 相似文献
7.
In a pseudocomplemented de Morgan algebra, it is shown that the set of kernel ideals is a complete Heyting lattice, and a necessary and sufficient condition that the set of kernel ideals is boolean (resp. Stone) is derived. In particular, a characterization of a de Morgan Heyting algebra whose congruence lattice is boolean (resp. Stone) is given. 相似文献
8.
在De Morgan代数上引入广义R0算子,举例说明了一般De Morgan代数中的广义R0算子不能构成t-模。引入强De Morgan代数的概念,讨论它的基本性质,证明强De Morgan代数L上的广义R0算子构成t-模(称为广义R0t-模)。给出若干重要反例,并证明强De Morgan代数上的广义R0t-模是左连续的。 相似文献
9.
Yu. M. Movsisyan V. A. Aslanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2013,48(6):241-246
The paper characterizes the class of subdirectly irreducible algebras satisfying hyperidentities of the variety of De Morgan algebras. Such algebras are called subdirectly irreducible De Morgan quasilattices. The suggested characterization is quite close to that of the classical case of subdirectly irreducible DeMorgan algebras. 相似文献
10.
Yu. M. Movsisyan V. A. Aslanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2013,48(5):233-240
The paper characterizes the algebras with hyperidentities of the variety of De Morgan algebras. For these algebras with two binary operations we prove a structure theorem. As a consequence, we obtain a finite base of the hyperidentities for the variety of De Morgan algebras having functional and objective ranks not exceeding three. 相似文献
11.
In this paper we shall introduce the variety WQS of weak‐quasi‐Stone algebras as a generalization of the variety QS of quasi‐Stone algebras introduced in [9]. We shall apply the Priestley duality developed in [4] for the variety N of ¬‐lattices to give a duality for WQS. We prove that a weak‐quasi‐Stone algebra is characterized by a property of the set of its regular elements, as well by mean of some principal lattice congruences. We will also determine the simple and subdirectly irreducible algebras (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
《Quaestiones Mathematicae》2013,36(3-4):273-290
Abstract A bispace is called strongly zero-dimensional if its bispace Stone—?ech compactification is zero—dimensional. To motivate the study of such bispaces we show that among those functorial quasi—uniformities which are admissible on all completely regular bispaces, some are and others are not transitive on the strongly zero-dimensional bispaces. This is in contrast with our result that every functorial admissible uniformity on the completely regular spaces is transitive precisely on the strongly zero-dimensional spaces. We then extend the notion of strong zero-dimensionality to frames and biframes, and introduce a De Morgan property for biframes. The Stone—Cech compactification of a De Morgan biframe is again De Morgan. In consequence, the congruence biframe of any frame and the Skula biframe of any topological space are De Morgan and hence strongly zero-dimensional. Examples show that the latter two classes of biframes differ essentially. 相似文献
13.
We provide a complete classification of solvable instances of the equational unification problem over De Morgan and Kleene algebras with respect to unification type. The key tool is a combinatorial characterization of finitely generated projective De Morgan and Kleene algebras. 相似文献
14.
将De Morgan代数的自同构群对De Morgan代数的作用,推广成抽象群对De Morgan代数的作用,引入了G-De Morgan代数的概念,讨论了G-De Morgan代数的G-同态、G-同余等性质,并研究了G-De Morgan代数的直积分解和次直不可约性. 相似文献
15.
Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices
with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the
paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly
their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented semilattices.
Supported by the Council of the Czech Government, MSM 6198959214. 相似文献
16.
In this paper we establish a Stone-type and a Birkhoff-type representation theorems for Boole–De Morgan algebras and prove that the free Boole–De Morgan algebra on n free generators is isomorphic to the Boole–De Morgan algebra of quasi-De Morgan functions of n variables. Also we introduce the concept of Zhegalkin polynomials for quasi-De Morgan functions and consider the representation problem of those functions by polynomials. 相似文献
17.
A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables. 相似文献
18.
本文研究了伪补MS-代数的同余关系.利用正则滤子和伪补代数的对偶窄间理论,得到了正则滤子所生成的同余关系的性质以及同余可换的伪补MS-代数类,从而推广了文献[9]的结果. 相似文献
19.
In this paper we investigate the sequence of subvarieties $ {\mathcal {SDH}_n} $of De Morgan Heyting algebras characterized by the identity xn(′*) ≈ x(n+1)(′*). We obtain necessary and sufficient conditions for a De Morgan Heyting algebra to be in $ {\mathcal {SDH}_1} $ by means of its space of prime filters, and we characterize subdirectly irreducible and simple algebras in $ {\mathcal {SDH}_1} $. We extend these results for finite algebras in the general case $ {\mathcal {SDH}_n} $. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献