共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Let be a regular and permutable variety and . Let . We get an explicit list L of polynomials such that C is a congruence class of some iff C is closed under all terms of L. Moreover, if is a finite similarity type, L is finite. If also is finite, all polynomials of L can be considered to be unary. We get a formula for the estimation of card L. The problem of deciding whether C is a congruence class of a finite algebra is in NP but for it is in P.
Received May 24, 1996; accepted in final form November 26, 1996. 相似文献
3.
John W. Snow 《Algebra Universalis》2007,57(1):3-14
A congruence lattice L of an algebra A is hereditary if every 0-1 sublattice of L is the congruence lattice of an algebra on A. Suppose that L is a finite lattice obtained from a distributive lattice by doubling a convex subset. We prove that every congruence lattice
of a finite algebra isomorphic to L is hereditary.
Presented by E. W. Kiss.
Received July 18, 2005; accepted in final form April 2, 2006. 相似文献
4.
A. M. Nurakunov 《Algebra Universalis》2008,58(3):357-372
The problem of characterizing the lattices of equational theories is still unsolved. In this paper we describe a class of monoids enriched by two unary operations and show that a lattice L is a lattice of equational theories if and only if L is isomorphic to a lattice of congruences of some enriched monoid belonging to .
The author was supported by INTAS grant 03-51-4110 and The Alexander von Humboldt Foundation. 相似文献
5.
Congruence properties in congruence permutable and in ideal determined varieties, with applications.
C. J. van. Alten 《Algebra Universalis》2005,53(4):433-449
We define a weak version of EDPC (equationally definable principal congruences), called EDPC*, that is shown to be preserved under varietal closure in congruence permutable varieties. We show that if
is a congruence permutable variety generated by a class
then
has EDPC iff
has EDPC* iff
has EDPC*. An equational condition is given which, if satisfied by
implies that
has the CEP (congruence extension property). Similar results are proved for ideal determined varieties. These results are applied to the variety of residuated lattices, with examples.Received January 15, 2004; accepted in final form October 8, 2004. 相似文献
6.
We describe explicitly the free algebras in the equational class generated by all algebras of binary relations with operations of union, composition, converse and reflexive transitive closure and neutral elements 0 (empty relation) and 1 (identity relation). We show the corresponding equational theory is decidable by reducing the problem to a question about regular sets. Similar results are given for two related equational theories.Presented by R. W. Quackenbush.Partially supported by a joint grant from the NSF and the Hungarian Academy of Sciences.Partially supported by a grant from the Hungarian National Foundation for Scientific Research and a joint grant from the NSF and the Hungarian Academy of Sciences.
v-semirings of 1-closed regular sets. On the basis of this characterization, we conjectured that a set of equational axioms for the variety RELv consists of equational axioms for the variety Lv and the equation (10). Recently, this conjecture has been proved in [6]. 相似文献
7.
Joohee Jeong 《Algebra Universalis》1992,29(3):441-448
We show that if a locally finite congruence modular varietyV is finitely decidable, thenV has to be congruence permutable.Presented by S. Burris. 相似文献
8.
The variety pOconsists of those algebras (L;?,?,f,*,0,1) where (L;?,?,f,0,1) is an Ockham algebra, (L;?,?,f,*,0,1) is a p-algebra, and the unary operations fand *. commute. For an algebra in pK ωwe show that the compact congruences form a dual Stone lattice and use this to determine necessary and sufficient conditions for a principal congruence to be complemented. We also describe the lattice of subvarieties of pK 1,1identifying therein the biggest subvariety in which every principal congruence is complemented, and the biggest subvariety in which the intersection of two principal congruences is principal. 相似文献
9.
Gábor Czédli 《Algebra Universalis》2007,57(1):63-73
A ternary term m(x, y, z) of an algebra is called a majority term if the algebra satisfies the identities m(x, x, y) = x, m(x, y, x) = x and m(y, x, x) = x. A congruence α of a finite algebra is called uniform if all of its blocks (i.e., classes) have the same number of elements. In particular, if all the α-blocks are two-element then α is said to be a 2-uniform congruence. If all congruences of A are uniform then A is said to be a uniform algebra. Answering a problem raised by Gr?tzer, Quackenbush and Schmidt [2], Kaarli [3] has recently proved that uniform finite lattices
are congruence permutable.
In connection with Kaarli’s result, our main theorem states that for every finite algebra A with a majority term any two 2-uniform congruences of A permute. Examples show that we can say neither “algebra” instead of “algebra with a majority term”, nor “3-uniform” instead
of “2-uniform”.
Given two nonempty sets A and B, each relation
gives rise to a pair of closure operators, which are called the Galois closures on A and B induced by ρ. Galois closures play an important role in many parts of algebra, and they play the main role in formal concept analysis
founded by Wille [4]. In order to prove our main theorem, we introduce a pair of smaller closure operators induced by ρ. These closure operators will hopefully find further applications in the future.
Dedicated to the memory of Kazimierz Głazek
Presented by E. T. Schmidt.
Received November 29, 2005; accepted in final form May 23, 2006.
This research was partially supported by the NFSR of Hungary (OTKA), grant no. T049433 and T037877. 相似文献
10.
Miroslav Ploš?ica 《Journal of Pure and Applied Algebra》2008,212(11):2503-2512
We present two examples of distributive algebraic lattices which are not isomorphic to the congruence lattice of any lattice. The first such example was discovered by F. Wehrung in 2005. One of our examples is defined topologically, the other one involves majority algebras. In particular, we prove that the congruence lattice of the free majority algebra on (at least) ℵ2 generators is not isomorphic to the congruence lattice of any lattice. Our method is a generalization of Wehrung’s approach, so that we are able to apply it to a larger class of distributive semilattices. 相似文献
11.
If T is an orthomodular lattice (OML), we denote by [T] the equational class generated by T. In this paper we characterize the finite OMLs T such that [T] covers some [MO
n
]. These OMLs T are the non-modular OMLs such that all proper sub-OMLs of T are modular. An OML satisfying that last property is called minimal. There exist infinitely many minimal OMLs provided by
quadratic spaces over finite fields. We describe them and give a new way to represent their Greechie diagrams in two separate
parts. Other methods to obtain finite minimal OMLs are given.
Received May 14, 2005; accepted in final form May 30, 2007. 相似文献
12.
Miroslav Ploščica 《Algebra Universalis》2005,54(3):323-335
We introduce the Local Separation Property (LSP) for distributive semilattices. We show that LSP holds in many semilattices
of the form Conc A, where A is a lattice. On the other hand, we construct an abstract example of a distributive lattice without LSP. Our research is
connected with the well known open problem whether every distributive algebraic lattice is isomorphic to the congruence lattice
of some lattice.
Received December 10, 2004; accepted in final form June 6, 2005. 相似文献
13.
Nathaël Alibaud 《Journal of Evolution Equations》2007,7(1):145-175
Using an integral formula of Droniou and Imbert (2005) for the fractional Laplacian, we define an entropy formulation for
fractal conservation laws with pure fractional diffusion of order λ ∈]0, 1]. This allows to show the existence and the uniqueness
of a solution in the L∞ framework. We also establish a result of controled speed of propagation that generalizes the finite propagation speed result
of scalar conservation laws. We finally let the non-local term vanish to approximate solutions of scalar conservation laws,
with optimal error estimates for BV initial conditions as Kuznecov (1976) for λ = 2 and Droniou (2003) for λ ∈]1, 2]. 相似文献
14.
Jie Fang 《Algebra Universalis》2006,55(2-3):277-292
The variety dpO consists of those algebras (L; ∧, ∨, f, *, +, 0, 1) with ∧, ∨ binary, f, *, + unary and 0, 1 nullary, and where (L; ∧, ∨, f, 0, 1) is an Ockham algebra and the unary operations f and * commute, f and+ commute. We describe completely the structure of the subdirectly irreducible algebras that belong to the subclass dpK1,1, characterised by the property f3 = f.
This paper is dedicated to Walter Taylor.
Received September 29, 2004; accepted in final form September 8, 2005. 相似文献
15.
罗从文 《数学物理学报(B辑英文版)》2011,31(3):1113-1122
Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained by Jie Fang on symmetric extended De Morgan algebras are generalized. 相似文献
16.
In this paper, the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras (see [13]). They show that every congruence relation θ on a decomposable MS-algebra L can be uniquely determined by a congruence pair (θ1, θ2), where θ1 is a congruence on the de Morgan subalgebra L?? of L and θ2 is a lattice congruence on the sublattice D(L) of L. They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L. Moreover, they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs. 相似文献
17.
John W. Snow 《Algebra Universalis》2000,44(1-2):169-185
Suppose is a set of operations on a finite set A. Define PPC() to be the smallest primitive positive clone on A containing . For any finite algebra A, let PPC#(A) be the smallest number n for which PPC(CloA) = PPC(Clo
n
A). S. Burris and R. Willard [2] conjectured that PPC#(A) ≤|A| when CloA is a primitive positive clone and |A| > 2. In this paper, we look at how large PPC#(A) can be when special conditions are placed on the finite algebra A. We show that PPC#(A) ≤|A| holds when the variety generated by A is congruence distributive, Abelian, or decidable. We also show that PPC#(A) ≤|A| + 2 if A generates a congruence permutable variety and every subalgebra of A is the product of a congruence neutral algebra and an Abelian algebra. Furthermore, we give an example in which PPC#(A) ≥|A| - 1)2 so that these results are not vacuous.
Received August 30, 1999; accepted in final form April 4, 2000. 相似文献
18.
In an earlier paper, the authors and H. Lakser proved that, for every lattice K and nontrivial congruence of K, there is an extension L of K such that is the restriction to K of a standard congruence on L. ?In this note, we give a very short proof of this result in a stronger form the lattice L we construct is sectionally complemented and it has only one nontrivial congruence, the standard congruence.
Received September 16, 1997; accepted in final form October 28, 1998. 相似文献
19.
J. M. Calabuig J. Rodríguez E. A. Sánchez-Pérez 《Integral Equations and Operator Theory》2009,64(1):21-33
Geometric and summability properties of the integration operator associated to a vector measure m can be translated in terms of structure properties of the space L1(m). In this paper we study the cases of the integration operator being: (i) p-concave on Lp(m), or (ii) positive p-summing on L1(m) (where ). We prove that (i) is equivalent to saying that L1(m) contains continuously the Lp space of a (non-negative scalar) control measure for m. On the other hand, we show that (ii) holds if and only if L1(m) is order isomorphic to the L1 space of a non-negative scalar measure.
J.M. Calabuig was supported by MEC and FEDER (MTM2005-08350-C03-03) and Generalitat Valenciana (GV/2007/191). J. Rodríguez was supported by MEC and FEDER (MTM2005-08379) and Generalitat Valenciana (GVPRE/2008/312). E.A. Sánchez-Pérez was supported by MEC and FEDER (MTM2006-11690-C02-01). 相似文献
20.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for
BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. 相似文献