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1.
This paper presents solutions or partial solutions for several problems in the theory of relation algebras. In a simple relation
algebra an element x satisfying the condition (a) must be an atom of . It follows that x must also be an atom in every simple extension of . Andréka, Jónsson and Németi [1, Problem 4] (see [12, Problem P5]) asked whether the converse holds: if x is an atom in every simple extension of a simple relation algebra, must it satisfy (a)? We show that the answer is “no”.?
The only known examples of simple relation algebras without simple proper extensions are the algebras of all binary relations
on a finite set. Jónsson proposed finding all finite simple relation algebras without simple proper extensions [12, Problem
P6]. We show how to construct many new examples of finite simple relation algebras that have no simple proper extensions, thus
providing a partial answer for this second problem. These algebras are also integral and nonrepresentable.? Andréka, Jónsson,
Németi [1, Problem 2] (see [12, Problem P7]) asked whether there is a countable simple relation algebra that cannot be embedded in a one-generated relation algebra.
The answer is “yes”. Givant [3, Problem 9] asked whether there is some k such that every finitely generated simple relation algebra can be embedded in a k-generated simple relation algebra. The answer is “no”.
Received November 27, 1996; accepted in final form July 3, 1997. 相似文献
2.
We show that, like singular cardinals, and weakly compact cardinals, Jensen's core model K for measures of order zero [4] calculates correctly the successors of Jónsson cardinals, assuming does not exist. Namely, if is a Jónsson cardinal then , provided that there is no non-trivial elementary embedding . There are a number of related results in ZFC concerning in V and inner models, for a Jónsson or singular cardinal.
Received: 8 December 1998 相似文献
3.
4.
Jan Tryba 《Israel Journal of Mathematics》1984,49(4):315-324
For a regular cardinal κ a Jónsson model of size κ+ is presented. We notice that every singular Jónsson cardinal κ with uncountable cofinality is the limit of some continuous
sequence of smaller Jónsson cardinals. An analogous statement holds if κ is an inaccessible Jónsson cardinal unless κ is Mahlo.
But we prove that the first Mahlo cardinal cannot be Jónsson. Some additional remarks are included. 相似文献
5.
6.
Yosuke Kuratomi 《代数通讯》2013,41(7):2747-2759
In this article, we introduce a generalization of quasi-discrete (a GQD-module) by using the notion of H-supplemented modules and investigate some properties of GQD-modules. First we consider some properties of a relative radical projectivity which is useful in analyzing the structure of H-supplemented modules. We apply them to the study of direct sums of GQD-modules. Moreover, we prove that any H-supplemented (lifting) module with finite internal exchange properly (FIEP) has an indecomposable decomposition and show that, for an H-supplemented (lifting) module, the finite exchange property implies the full exchange property. 相似文献
7.
Bill Sands 《Algebra Universalis》1977,7(1):211-217
A latticeL satisfies thebounded epimorphism condition if wheneverM is a lattce and ϕ:M →L is a bounded epimorphism, there exists a homomorphismι:L →M such that ιϕ=id
L
. we show that the class of finite lattices satisfying the bounded epimorphism condition is properly contained in the class
of finite lattices satisfying Whitman's condition (W). We also introduce a property defined for finite lattices that is sufficient
to imply the bounded epimorphism condition.
Presented by B. Jónsson. 相似文献
8.
Marcel Wild 《Algebra Universalis》2018,79(4):79
A famous Theorem of Pudlak and T?ma states that each finite lattice L occurs as sublattice of a finite partition lattice. Here we derive, for modular lattices L, necessary and sufficient conditions for cover-preserving embeddability. Aspects of our work relate to Bjarni Jónsson. 相似文献
9.
10.
Wieslaw Dziobiak 《Algebra Universalis》1981,13(1):148-156
As was indicated to me by Prof. A. Wroński, the following problem was suggested by Prof. B. Jónsson: is every subvariety of the variety of a finite algebra generated by a finite algebra? In this paper we solve this problem in the negative by constructing a finite algebra that generates a variety having 2x 0 subvarieties. 相似文献
11.
In Palmigiano and Re (J Pure Appl Algebra 215(8):1945–1957, 2011), spatial SGF-quantales are axiomatically introduced and proved to be representable as sub unital involutive quantales of quantales arising from set groupoids. In the present paper, spatial SGF-quantales of this class are shown to be optimally representable as unital involutive quantales of relations. The results of the present paper have several aspects in common with Jónsson and Tarski’s representation theory for relation algebras (Jónsson and Tarski, Am J Math 74(2):127–162, 1952). 相似文献
12.
《Annals of Pure and Applied Logic》1988,37(2):179-204
We survey the definition and fundamental properties of the family of short core models, which extend the core model K of Dodd and Jensen to include α-sequences of measurable cardinals (α ϵ On). The theory is applied to various combinatorial principles to get lower bounds for their consistency strengths in terms of the existence of sequences of measurable cardinals. We consider instances of Chang's conjecture, ‘accessible’ Jónsson cardinals, the free subset property for small cardinals, a canonization property of ωω, and a non-closure property of elementary embeddings of the universe. In some cases, equiconsistencies are obtained. 相似文献
13.
In this paper, we deal with the classification of the irreducible Z-graded and Z
2-graded modules with finite dimensional homogeneous subspaces for the q analog Virasoro-like algebra L. We first prove that a Z-graded L-module must be a uniformly bounded module or a generalized highest weight module. Then we show that an irreducible generalized
highest weight Z-graded module with finite dimensional homogeneous subspaces must be a highest (or lowest) weight module and give a necessary
and sufficient condition for such a module with finite dimensional homogeneous subspaces. We use the Z-graded modules to construct a class of Z
2-graded irreducible generalized highest weight modules with finite dimensional homogeneous subspaces. Finally, we classify
the Z
2-graded L-modules. We first prove that a Z
2-graded module must be either a uniformly bounded module or a generalized highest weight module. Then we prove that an irreducible
nontrivial Z
2-graded module with finite dimensional homogeneous subspaces must be isomorphic to a module constructed as above. As a consequence,
we also classify the irreducible Z-graded modules and the irreducible Z
2-graded modules with finite dimensional homogeneous subspaces and center acting nontrivial.
Supported by the National Science Foundation of China (No 10671160), the China Postdoctoral Science Foundation (No. 20060390693),
the Specialized Research fund for the Doctoral Program of Higher Education (No.20060384002), and the New Century Talents Supported
Program from the Education Department of Fujian Province. 相似文献
14.
An error in a proof of a correct theorem in the classic paper, Boolean Algebras with Operators, Part I, by Jónsson and Tarski is discussed. 相似文献
15.
F. E. A. Johnson 《K-Theory》2005,34(2):141-150
In [F.E.A. Johnson, Stable Modules and the D(2)-Problem, LMS Lecture Notes In Mathematics, vol. 301, CUP (2003)], for finite groups G, we gave a parametrization of the stable class of the augmentation ideal of Z[G] in terms of stably free modules. Whilst the details of this parametrization break down immediately for infinite groups,
nevertheless one may hope to find parallel arguments for restricted classes of infinite groups. Subject to the restriction
that Ext1(Z, Z[G]) = 0, we parametrize the minimal level in Ω1(Z) by means of stably free modules and give a lower estimate for the size of Ω1(Z). 相似文献
16.
George F. McNulty 《Algebra Universalis》1982,15(1):115-125
For countable languages, we completely describe those cardinals κ such that there is an equational theory which covers exactly
κ other equational theories. For this task understanding term finite theories is helpful. A theoryT isterm finite provided {ψ:Tτϕ≈ψ} is finite for all terms ϕ. We develop here some fundamental properties of term finite theories and use them, together
with Ramsey's Theorem, to prove that any finitely based term finite theory covers only finitely many others. We also show
that every term finite theory possesses an independent base and that there are
such theories whose pairwise joins are not term finite.
The paper was written with the support of NSF Grant MCS-80-01778.
Presented by B. Jónsson. Received July 22, 1980. Accepted for publication in final form March 19, 1981. 相似文献
17.
Christian Herrmann 《Algebra Universalis》2013,70(2):163-174
We review (and slightly extend) Bjarni Jónsson’s results on representations of arguesian lattices that are complemented, of low height, or of simple gluing structure. 相似文献
18.
Mai Gehrke 《Algebra Universalis》2018,79(3):63
This note aims to highlight some of the conceptual contributions to duality theory made by Bjarni Jónsson through the theory of canonical extensions. 相似文献
19.
R D Giri 《Proceedings Mathematical Sciences》1984,93(1):53-58
The concept of residuation in varieties introduced by Neumann [5] and reoriented and developed by Jónsson is further studied in this paper. 相似文献
20.
AbstractThe aim of the present paper is to introduce and study the dual concepts of weakly automorphism invariant modules and essential tightness. These notions are non-trivial generalizations of both weakly projectivity, dual automorphism invariant property and cotightness. We obtain certain relations between weakly projective modules, weakly dual automorphism invariant modules and superfluous cotight modules. It is proved that: (1) for right perfect rings, every module is a direct summand of a weakly dual automorphism invariant module and (2) weakly dual automorphism invariant modules are precisely superfluous cotight modules. 相似文献