1,864 research outputs found
Generalized U-factorization in Commutative Rings with Zero-Divisors
Recently substantial progress has been made on generalized factorization
techniques in integral domains, in particular -factorization. There has
also been advances made in investigating factorization in commutative rings
with zero-divisors. One approach which has been found to be very successful is
that of U-factorization introduced by C.R. Fletcher. We seek to synthesize work
done in these two areas by generalizing -factorization to rings with
zero-divisors by using the notion of U-factorization.Comment: 16 pages, to appear in Rocky Mountain Journal of Mathematic
Generalized Irreducible Divisor Graphs
In 1988, I. Beck introduced the notion of a zero-divisor graph of a
commutative rings with . There have been several generalizations in recent
years. In particular, in 2007 J. Coykendall and J. Maney developed the
irreducible divisor graph. Much work has been done on generalized
factorization, especially -factorization. The goal of this paper is to
synthesize the notions of -factorization and irreducible divisor graphs
in domains. We will define a -irreducible divisor graph for non-zero
non-unit elements of a domain. We show that by studying -irreducible
divisor graphs, we find equivalent characterizations of several finite
-factorization properties.Comment: 17 pages, 2 figures, to appear in Communications in Algebr
The antibiotic sensitivity patterns and plasmid DNA content of gram-negative anaerobic bacteria isolated in Palmerston North, New Zealand : a thesis presented in partial fulfilment of the requirements for the degree of Masters in Science at Massey University
One hundred and seven Gram-negative bacteria, including 65 Bacteroides species, 28 fusobacteria and
14 veillonellae were isolated from 17 oral infections treated in two dental surgeries in Palmerston North. These bacteria, plus 37 isolates belonging to the
B. fragilis group received from Palmerston North hospital, were surveyed for their antibiotic sensitivity levels, and their plasmid DNA content.
The hospital isolates of the B. fragilis group were found to have sensitivity levels comparable
with those of B. fragilis group isolates reported in the literature recently. The oral isolates were more sensitive to penicillin, cefoxitin, and tetracycline than isolates of the same species reported in the literature.
Half the hospital isolates had plasmids, which were all between 8.5 and 2.7 kilobases (kb) in size except for one 60, and one 43 kb plasmid. Comparatively few of the oral anaerobes had plasmids. One Fusobacterium russii isolate had four plasmids, and five Bacteroides
isolates had one plasmid each. These five Bacteroides isolates came from two specimens, R5 and R6.
Restriction enzyme analysis of all plasmids revealed that the three 5.6 kb plasmids from sample R5 may be related to a group of 5.8 kb plasmids harboured by four of the hospital isolates. Two different
species of Bacteroides isolated from sample R5 harboured the 5.6 kb plasmid, and two species of the B. fragilis group bacteria harboured the 5.8 kb plasmid.
Plasmid DNA isolated from two tetracycline resistant hospital isolates was used to transform restriction negative E. coli to a low level of tetracycline resistance
Cell-Like Equivalences and Boundaries of CAT(0) Groups
In 2000, Croke and Kleiner showed that a CAT(0) group G can admit more than
one boundary. This contrasted with the situation for word hyperbolic groups,
where it was well-known that each such group admitted a unique boundary---in a
very stong sense. Prior to Croke and Kleiner's discovery, it had been observed
by Geoghegan and Bestvina that a weaker sort of uniquness does hold for
boundaries of torsion free CAT(0) groups; in particular, any two such
boundaries always have the same shape. Hence, the boundary really does carry
significant information about the group itself. In an attempt to strengthen the
correspondence between group and boundary, Bestvina asked whether boundaries of
CAT(0) groups are unique up to cell-like equivalence. For the types of space
that arise as boundaries of CAT(0) groups, this is a notion that is weaker than
topological equivalence and stronger than shape equivalence. In this paper we
explore the Bestvina Cell-like Equivalence Question. We describe a
straightforward strategy with the potential for providing a fully general
positive answer. We apply that strategy to a number of test cases and show that
it succeeds---often in unexpectedly interesting ways.Comment: 21 pages, 5 figure
Examples of Non-Rigid CAT(0) Groups from the Category of Knot Groups
C Croke and B Kleiner have constructed an example of a CAT(0) group with more
than one visual boundary. J Wilson has proven that this same group has
uncountably many distinct boundaries. In this article we prove that the knot
group of any connected sum of two non-trivial torus knots also has uncountably
many distinct CAT(0) boundaries.Comment: 16 pages, 2 figure
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