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1.
The concept of a semiprime ideal in a poset is introduced. The relations between the semiprime (prime) ideals of a poset and
the ideals of the set of all ideals of the poset are established. A result analogous to Separation Theorem is obtained in
respect of semiprime ideals. Further, a generalization of Stone’s Separation Theorem for posets is obtained in respect of
prime ideals. Some counterexamples are also given.
相似文献
2.
I. Heckenberger 《Algebras and Representation Theory》2008,11(2):115-132
The concept of arithmetic root systems is introduced. It is shown that there is a one-to-one correspondence between arithmetic
root systems and Nichols algebras of diagonal type having a finite set of (restricted) Poincaré–Birkhoff–Witt generators.
This has strong consequences for both objects. As an application all rank 2 Nichols algebras of diagonal type having a finite
set of (restricted) Poincaré–Birkhoff–Witt generators are determined.
Supported by the European Community under a Marie Curie Intra-European Fellowship. 相似文献
3.
We study complementation in bounded posets. It is known and easy to see that every complemented distributive poset is uniquely complemented. The converse statement is not valid, even for lattices. In the present paper we provide conditions that force a uniquely complemented poset to be distributive. For atomistic resp. atomic posets as well as for posets satisfying the descending chain condition we find sufficient conditions in the form of so-called LU-identities. It turns out that for finite posets these conditions are necessary and sufficient. 相似文献
4.
We prove that the poset algebra of every scattered poset with finite width is embeddable in the poset algebra of a well ordered poset.Mathematics Subject Classification (2000):Primary 03G05, 06A06, 06A11; Secondary 08A05, 54G12 相似文献
5.
A structure is said to be ‘Okhuma’ if its automorphism group acts on it uniquely transitively, or slightly generalizing this,
if its automorphism group acts uniquely transitively on each orbit. In this latter case we can think of the orbits as ‘colours’.
Okhuma chains and related structures have been studied by Okhuma and others. Here we generalize their results to coloured
chains, and give some constructions resulting from this of Okhuma graphs and digraphs.
Mathematics Subject Classifications (2000) 06A05, 06F15. 相似文献
6.
In the first section of this paper, we prove an analogue of Stone’s Theorem for posets satisfying DCC by using semiprime ideals. We also prove the existence of prime ideals in atomic posets in which atoms are dually distributive. Further, it is proved that every maximal non-dense (non-principal) ideal of a 0-distributive poset (meet-semilattice) is prime. The second section focuses on the characterizations of (minimal) prime ideals in pseudocomplemented posets. The third section deals with the generalization of the classical theorem of Nachbin. In fact, we prove that a dually atomic pseudocomplemented, 1-distributive poset is complemented if and only if the poset of prime ideals is unordered. In the last section, we have characterized 0-distributive posets by means of prime ideals and minimal prime ideals. 相似文献
7.
We study the so-called Skorokhod reflection problem (SRP) posed for real-valued functions defined on a partially ordered set
(poset), when there are two boundaries, considered also to be functions of the poset. The problem is to constrain the function
between the boundaries by adding and subtracting nonnegative nondecreasing (NN) functions in the most efficient way. We show
existence and uniqueness of its solution by using only order theoretic arguments. The solution is also shown to obey a fixed
point equation. When the underlying poset is a σ-algebra of subsets of a set, our results yield a generalization of the classical Jordan–Hahn decomposition of a signed measure.
We also study the problem on a poset that has the structure of a tree, where we identify additional structural properties
of the solution, and on discrete posets, where we show that the fixed point equation uniquely characterizes the solution.
Further interesting posets we consider are the poset of real n-vectors ordered by majorization, and the poset of n × n positive semidefinite real matrices ordered by pointwise ordering of the associated quadratic forms. We say a function on
a poset is of bounded variation if it can be written as the difference of two NN functions. The solution to the SRP when the upper and lower boundaries are
the identically zero function corresponds to the most efficient or minimal such representation of a function of bounded variation.
Minimal representations for several important functions of bounded variation on several of the posets mentioned above are
determined in this paper.
A version of this paper was presented at the Applied Probability Workshop, in the Mathematisches Forschungsinstitut Oberwolfach,
December 2003 (organized by V. Schmidt, A. Hordijk and F. Baccelli); the authors are grateful for the invitation which gave
them the opportunity to make substantial progress in finalizing this work in the uniquely wonderful research atmosphere at
Oberwolfach.
Research supported by DARPA grant N66001-00-C-8062, ONR grant N00014-1-0637 and NSF grant ECS 0123512.
This work was supported in part by NSF grant ANI-9903495, the INTAS-00-265 project, and a Carathéodory research award. 相似文献
8.
Leonardo Mora 《Bulletin of the Brazilian Mathematical Society》2011,42(1):25-43
We present a real multidimensional version of the Schwarz Lemma on a bounded convex domain D of ℝ
n
endowed with the Hilbert metric. We provide as an application an extension of a Birkhoff’s Theorem on mappings contracting
the Hilbert metric. 相似文献
9.
Christos A. Athanasiadis 《Journal of Algebraic Combinatorics》2012,35(3):373-388
A certain inequality is shown to hold for the values of the M?bius function of the poset obtained by attaching a maximum element
to a lower Eulerian Cohen–Macaulay poset. In two important special cases, this inequality provides partial results supporting
Stanley’s nonnegativity conjecture for the toric h-vector of a lower Eulerian Cohen–Macaulay meet-semilattice and Adin’s nonnegativity conjecture for the cubical h-vector of a Cohen–Macaulay cubical complex. 相似文献
10.
Rodin and Sullivan (1987) proved Thurston’s conjecture that a scheme based on the Circle Packing Theorem converges to the
Riemann mapping, thereby providing a refreshing geometric view of Riemann’s Mapping Theorem. We now present a new proof of
the Rodin–Sullivan theorem. This proof is based on the argument principle, and has the following virtues.
1. It applies to more general packings. The Rodin–Sullivan paper deals with packings based on the hexagonal combinatorics.
Later, quantitative estimates were found, which also worked for bounded valence packings. Here, the bounded valence assumption
is unnecessary and irrelevant.
2. Our method is rather elementary, and accessible to non-experts. In particular, quasiconformal maps are not needed. Consequently,
this gives an independent proof of Riemann’s Conformal Mapping Theorem. (The Rodin–Sullivan proof uses results that rely on
Riemann’s Mapping Theorem.)
3. Our approach gives the convergence of the first and second derivatives, without significant additional difficulties. While
previous work has established the convergence of the first two derivatives for bounded valence packings, now the bounded valence
assumption is unnecessary.
Oblatum 15-V-1995 & 13-XI-1995 相似文献
11.
We give an alternate proof of Schnyder’s Theorem, that the incidence poset of a graph G has dimension at most three if and only if G is planar. 相似文献
13.
Theorem 2.2 stated a monoidal isomorphism between the comodule categories of two bialgebroids in a Hopf algebroid. The proof
of Theorem 2.2 was based on the journal version of Brzeziński (Ann Univ Ferrara Sez VII (NS) 51:15–27, 2005, Theorem 2.6), whose proof turned out to contain an unjustified step. Here we show that all other results in our paper remain
valid if we drop unverified Theorem 2.2, and return to an earlier definition of a comodule of a Hopf algebroid that distinguishes
between comodules of the two constituent bialgebroids. 相似文献
14.
Elias David 《Algebra Universalis》2002,47(1):95-102
We define the -ideals of a poset – or equally of a quasi-ordered set – for various collections of subsets and corresponding -ideal continuity for functions. This leads us to a choice-free -ideal continuous imbedding of a poset into a -join complete poset with an appropriate universal mapping property. Topological applications include the imbedding of Scott
spaces and Alexandrov spaces into up-complete Scott spaces.
Received May 26, 1998; accepted in final form June 28, 2001. 相似文献
15.
Yu Quan Xie 《数学学报(英文版)》2008,24(12):1965-1984
In this paper, we study the basic properties of stationary transition probability of Markov processes on a general measurable space (E, δ), such as the continuity, maximum probability, zero point, positive probability set,standardization, and obtain a series of important results such as Continuity Theorem, Representation Theorem, Levy Theorem and so on. These results are very useful for us to study stationary tri-point transition probability on a general measurable space (E, δ). Our main tools such as Egoroff's Theorem, Vitali-Hahn-Saks's Theorem and the theory of atomic set and well- posedness of measure are also very interesting and fashionable. 相似文献
16.
In this paper, we study some of properties of the min-max compositions of fuzzy matrices and give out a dual theorem (to Theorem 3 of [4]) about the convergence of the power sequence of min-max compositions of fuzzy matrices.AMS Subject Classification (2000) 15A45 06A06 04A72 相似文献
17.
We prove versions of the Dual Ramsey Theorem and the Dual Ellentuck Theorem for families of partitions which are defined
in terms of games.
Received: 8 July 1999 Published online: 19 December 2002
RID="*"
ID="*" The author wishes to thank the Swiss National Science Foundation for supporting him.
The authors thank the referee for helpful comments.
Mathematics Subject Classification (2000): 03E02, 05D10, 03E35
Key words or phrases: Dual Ramsey Theorem – Dual Ellentuck Theorem – Partitions – Games 相似文献
18.
Combining the arguments developed in the works of D. A. Goldston,S. W. Graham, J. Pintz, and C. Y. Yildirim [Preprint, 2005,arXiv: math.NT/506067] and Y. Motohashi [Number theory in progress– A. Schinzel Festschrift (de Gruyter, 1999) 1053–1064]we introduce a smoothing device to the sieve procedure of Goldston,Pintz, and Yildirim (see [Proc. Japan Acad. 82A (2006) 61–65]for its simplified version). Our assertions embodied in Lemmas3 and 4 of this article imply that a natural extension of aprime number theorem of E. Bombieri, J. B. Friedlander, andH. Iwaniec [Theorem 8 in Acta Math. 156 (1986) 203–251]should give rise infinitely often to bounded differences betweenprimes, that is, a weaker form of the twin prime conjecture. 相似文献
19.
Craig R. Guilbault 《Discrete and Computational Geometry》2010,43(4):951-954
The Topological Radon Theorem states that, for every continuous function from the boundary of a (d+1)-dimensional simplex into ℝ
n
, there exists a pair of disjoint faces in the domain whose images intersect in ℝ
n
. The similarity between that result and the classical Borsuk–Ulam Theorem is unmistakable, but a proof that the Topological
Radon Theorem follows from Borsuk–Ulam is not immediate. In this note we provide an elementary argument verifying that implication. 相似文献
20.
Peter C. Fishburn 《Order》1989,6(2):159-173
A class of finite partially ordered sets isinvertible if the inverse (dual) of every poset in the class is in the class, and iszero-augmentable if the addition of a new element below all others yields a poset in the class for each member. This paper demonstrates that certain classes of posets that have representations byN-gons in the plane ordered by proper inclusion are neither invertible nor zero-augmentable.
AMS subject classification (1980). 06A10. 相似文献