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1.
Samuel S. Holland 《Israel Journal of Mathematics》1987,57(3):365-374
We construct examples of Baer ordered *-fields of the first kind of every dimension 4
n
,n=1,2,…. 相似文献
2.
Yu. L. Ershov 《Algebra and Logic》1994,33(4):205-215
It is stated that if a Boolean family W of valuation rings of a field F satisfies the block approximation property (BAP) and a global analog of the Hensel-Rychlick property (THR), in which case F, W is called an RC*-field, then F is regularly closed with respect to the family W (The-orem 1). It is proved that every pair F, W, where W is a weakly Boolean family of valuation rings of a field F, is embedded in the RC*-field F0, W0 in such a manner that R0 R0 F, R0 W0 is a continuous map, W0 is homeomorphic over W to a given Boolean space, and R0 is a superstructure of R0 F for every R0 W0 (Theorem 2).Translated fromAlgebra i Logika, Vol. 33, No. 4, pp. 367–386, July-August, 1994. 相似文献
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We characterize Leavitt path algebras which are Rickart, Baer, and Baer ?-rings in terms of the properties of the underlying graph. In order to treat non-unital Leavitt path algebras as well, we generalize these annihilator-related properties to locally unital rings and provide a more general characterizations of Leavitt path algebras which are locally Rickart, locally Baer, and locally Baer ?-rings. Leavitt path algebras are also graded rings and we formulate the graded versions of these annihilator-related properties and characterize Leavitt path algebras having those properties as well.Our characterizations provide a quick way to generate a wide variety of examples of rings. For example, creating a Baer and not a Baer ?-ring, a Rickart ?-ring which is not Baer, or a Baer and not a Rickart ?-ring, is straightforward using the graph-theoretic properties from our results. In addition, our characterizations showcase more properties which distinguish behavior of Leavitt path algebras from their -algebra counterparts. For example, while a graph -algebra is Baer (and a Baer ?-ring) if and only if the underlying graph is finite and acyclic, a Leavitt path algebra is Baer if and only if the graph is finite and no cycle has an exit, and it is a Baer ?-ring if and only if the graph is a finite disjoint union of graphs which are finite and acyclic or loops. 相似文献
4.
D. J. Foulis 《Mathematische Annalen》1967,175(4):297-302
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This paper investigates dagger kernel categories which are considered first by Crown (J Nat Sci Math 15:11?C25, 1975) and used by Heunen and Jacobs (Order 27:177?C212, 2010) in their study of quantum logic from the perspective of categorical logic. The inverse Baer*-categories with splitting projections as special dagger kernel categories have a central place in our investigations. The inverse Baer*-categories with splitting and closed projections are Boolean and therefore the subobject lattices of such categories are representing classical logics. Examples are presented at every stage of our investigations. 相似文献
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Victor Pambuccian 《Mathematical Logic Quarterly》2010,56(1):29-34
We prove that, in the framework of ordered geometry, the inner form of the Pasch axiom ( IP ) does not imply its outer form ( OP ). We also show that OP can be properly split into IP and the weak Pasch axiom ( WP ) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Harm Pralle 《Journal of Geometry》2004,81(1-2):144-154
If K is a blocking set of a projective space
and P a point not in K, then the projection of K from P onto a hyperplane of
not containing P is a blocking set of . Projecting a blocking set K of PG(3, q2) from two different points P0, P1 onto a plane neither containing P0 nor P1, the intersection of the two cones with vertices P0 and P1 and bases the corresponding projections onto should constitute a big part of the blocking set. Looking for non-trivial blocking sets, the bases contain each a Baer subplane of . Hence the intersection of the two Baer cones over these Baer subplanes with the vertices P0 and P1 are part of the blocking set K in PG(3, q2). In this article, we describe the intersection configurations of two Baer cones in PG(3, q2). 相似文献
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In this article, the structure of the collineation groups which fix point-Baer subplanes in vector space nets over skewfields is completely determined. The theory depends on whether there are one, two, or at least three point-Baer subplanes sharing the same parallel classes and a common point.The authors are indebted to the referee for helpful suggestions. 相似文献
17.
Ronald D. Baker Jeremy M. Dover Gary L. Ebert Kenneth L. Wantz 《Journal of Geometry》2000,67(1-2):23-34
For any odd integern 3 and prime powerq, it is known thatPG(n–1, q2) can be partitioned into pairwise disjoint subgeometries isomorphic toPG(n–1, q) by taking point orbits under an appropriate subgroup of a Singer cycle ofPG(n–1, q2). In this paper, we construct Baer subgeometry partitions of these spaces which do not arise in the classical manner. We further illustrate some of the connections between Baer subgeometry partitions and several other areas of combinatorial interest, most notably projective sets and flagtransitive translation planes. 相似文献
18.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
19.
A right module M over a ring R is called feebly Baer if, whenever xa = 0 with x ∈ M and a ∈ R, there exists e2 = e ∈ R such that xe = 0 and ea = a. The ring R is called feebly Baer if RR is a feebly Baer module. These notions are motivated by the commutative analog discussed in a recent paper by Knox, Levy, McGovern, and Shapiro [6]. Basic properties of feebly Baer rings and modules are proved, and their connections with von Neumann regular rings are addressed. 相似文献
20.
Regular rings and Baer rings 总被引:2,自引:0,他引:2
Prof. Ancel C. Mewborn 《Mathematische Zeitschrift》1971,121(3):211-219