Current Search: info:fedora/islandora:personCModel (x) » English (x) » Mathematics (x)
View All Items
 Title
 EVERY FINITE ABELIAN GROUP IS A BRAUER GROUP.
 Creator
 FORD, TIMOTHY JOE., Colorado State University
 Abstract/Description

Let A be the affine coordinate ring of the plane nodal cubic curve y('2) = x('2)(x+1) over the complex number field. That is, A = (//C){x, y}/(y('2)  x('2)(x+1)). Let n (GREATERTHEQ) 2 be an integer, let f(,n) = zy('n1)  x('n) and let B(,n) be the subring of the localized ring (//C){x, y, z}{1/f(,n)} consisting of all fractions g/f(,n)('r) such that g is a homogeneous polynomial of degree rn, r (GREATERTHEQ) 0. Then we show that the Brauer group of A (CRTIMES)(,(//C)) B(,n) is cyclic of...
Show moreLet A be the affine coordinate ring of the plane nodal cubic curve y('2) = x('2)(x+1) over the complex number field. That is, A = (//C){x, y}/(y('2)  x('2)(x+1)). Let n (GREATERTHEQ) 2 be an integer, let f(,n) = zy('n1)  x('n) and let B(,n) be the subring of the localized ring (//C){x, y, z}{1/f(,n)} consisting of all fractions g/f(,n)('r) such that g is a homogeneous polynomial of degree rn, r (GREATERTHEQ) 0. Then we show that the Brauer group of A (CRTIMES)(,(//C)) B(,n) is cyclic of order n. Thus, every finite cyclic group is the Brauer group of a threedimensional noetherian integral domain. Since every finite abelian group G is a direct sum of cyclic groups we see that any G is the Brauer group of the threedimensional noetherian ring A (CRTIMES)(,(//C)) (B(,n(,1)) (CRPLUS)...(CRPLUS)B(,n(,r))) for suitable choices of n(,i)., Using cohomological techniques we investigate the Brauer group of Y x (,k)' where Y is a scheme over a field k. We give sufficient conditions on Y so that the Brauer group of Y x ' is equal to the Brauer group of Y. In particular, equality holds if Y has dimension one over k and the characteristic of k is zero., Let R be a commutative noetherian connected regular ring. Using excision sequences we show that the sequence of groups, 0 (>) B(R{x}) (>) B{R{x, 1/x}) (>) H(,Z)('3)(X, G(,m)) (>) 0, is exact where X = Proj R{x(,0), x(,1)} and Z = Spec R is the closed subscheme x(,0) = 0. If we further assume that R contains the field of rational numbers, then B(R{x, 1/x}) = B(R) (CRPLUS) Hom(G, / ) where G is the Galois groupof R.
Show less  Date Issued
 1980, 1980
 PURL
 http://purl.flvc.org/fcla/dt/40555
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 FINITE GROUPS ADMITTING FIXEDPOINTFREE AUTOMORPHISMS.
 Creator
 HOFFMAN, FREDERICK., University of Virginia
 Date Issued
 1964, 1964
 PURL
 http://purl.flvc.org/fcla/dt/40291
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 THE GOEDEL SPEEDUP PHENOMENON.
 Creator
 Solomon, Martin K., Stevens Institute of Technology
 Date Issued
 1976, 1976
 PURL
 http://purl.flvc.org/fcla/dt/40501
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 LOCAL FACTORIZATION OF NONSINGULAR BIRATIONAL MORPHISMS IN DIMENSION GREATER THAN TWO (REGULAR LOCAL RINGS, DESCENDING CHAIN CONDITION, RATIONAL SINGULARITY).
 Creator
 JOHNSTON, BERNARD LAWRENCE., Purdue University
 Abstract/Description

The Local Factorization Theorem of Zariski and Abhyankar implies that between a given pair of 2dimensional regular local rings, S (GREATERTHEQ) R, having the same quotient field, every chain of regular local rings must be finite in length. It is shown that this property extends to every such pair of regular local rings, regardless of dimension. Examples are given to show that this does not hold if "regular" is weakened to various statements, including "Gorenstein", "rational singularity",...
Show moreThe Local Factorization Theorem of Zariski and Abhyankar implies that between a given pair of 2dimensional regular local rings, S (GREATERTHEQ) R, having the same quotient field, every chain of regular local rings must be finite in length. It is shown that this property extends to every such pair of regular local rings, regardless of dimension. Examples are given to show that this does not hold if "regular" is weakened to various statements, including "Gorenstein", "rational singularity", and "normal". More generally, it is shown that the set of ndimensional regular local rings birationally containing an arbitrary integral domain must satisfy the descending chain condition. Some conditions which imply a uniform bound on the lengths of certain chains between two fixed ndimensional regular local rings, as above, are given. Finally, a new class, containing infinitely many minimal regular local overrings containing a fixed regular local ring, is presented.
Show less  Date Issued
 1986, 1986
 PURL
 http://purl.flvc.org/fcla/dt/40632
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 MODULES OVER ZG, A NONABELIAN GROUP OF ORDER PQ.
 Creator
 Klingler, Lee, The University of Wisconsin  Madison
 Abstract/Description

Let G be a nonabelian group of order pq (p and q primes). In this paper we solve the problem of describing all isomorphism classes of finitely generated left ZGmodules, where ZG is the integral group ring of G. We consider ZGmodules in general and not merely lattices., Our main result is to define a function "class" cl( ) from the category of (finitely generated) left ZGmodules into the finite set of isomorphism classes of fractional (not necessarily full) left ZGmodules in the quotient...
Show moreLet G be a nonabelian group of order pq (p and q primes). In this paper we solve the problem of describing all isomorphism classes of finitely generated left ZGmodules, where ZG is the integral group ring of G. We consider ZGmodules in general and not merely lattices., Our main result is to define a function "class" cl( ) from the category of (finitely generated) left ZGmodules into the finite set of isomorphism classes of fractional (not necessarily full) left ZGmodules in the quotient ring QG of ZG. We define cl( ) in such a way that, for arbitrary finitely generated left ZGmodules M and N, M (TURNEQ) N iff cl(M) = cl(N) and (')M(,t) (TURNEQ) (')N(,t) (tadic completion) for all primes t., With CLS(ZG) the image of the function cl( ), we define an operation "+" on CLS(ZG) in such a way that cl(M (CRPLUS) N) = cl(M) + cl(N). CLS(ZG) forms a semigroup under this operation and decomposes as the disjoint union of a finite collection of subgroups, where each subgroup is itself just a genus of fractional ideals. We show that each of these subgroups (and consequently each genus) has order dividing the order of the locally free class group of ZG., We apply this numerical information to questions of local versus global isomorphism and direct sum decompositions of finitely generated left ZGmodules. In particular (for G as above), we determine those primes t such that the KrullSchmidt theorem holds for finitely generated Z(,t)Gmodules (localization at t). We determine necessary and sufficient conditions that cancellation hold for finitely generated ZGmodules, and we calculate a "power cancellation exponent" e such that M (CRPLUS) X = M (CRPLUS) Y implies X('(e)) = Y('(e)).
Show less  Date Issued
 1984, 1984
 PURL
 http://purl.flvc.org/fcla/dt/40597
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 ON ABSOLUTELY TORSIONFREE RINGS AND KERNEL FUNCTORS.
 Creator
 VIOLAPRIOLI, JORGE E., Rutgers The State University of New Jersey  New Brunswick
 Date Issued
 1973, 1973
 PURL
 http://purl.flvc.org/fcla/dt/40474
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 ON THE MONOTONE EXTENSION PROPERTY.
 Creator
 MECH, WILLIAM PAUL., University of Illinois at UrbanaChampaign
 Date Issued
 1970, 1970
 PURL
 http://purl.flvc.org/fcla/dt/40437
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 PARTIAL GEOMETRIC LATTICES (DESIGNS).
 Creator
 MEYEROWITZ, AARON DAVID., Colorado State University
 Abstract/Description

A partial geometric lattice, PGL, is a finite ranked lattice of rank m which, aside from certain nontriviality conditions, satisfies the following condition, as do its intervals: If p is a point and l a line, the number of points q l such that p V q has rank k depends only on the rank of p V l., In case m = 3, this is a partial geometry as defined by Bose. In a PGL, any two intervals bounded by an ispace and an i + sspace contain the same number of i + kspaces. Those numbers determine the...
Show moreA partial geometric lattice, PGL, is a finite ranked lattice of rank m which, aside from certain nontriviality conditions, satisfies the following condition, as do its intervals: If p is a point and l a line, the number of points q l such that p V q has rank k depends only on the rank of p V l., In case m = 3, this is a partial geometry as defined by Bose. In a PGL, any two intervals bounded by an ispace and an i + sspace contain the same number of i + kspaces. Those numbers determine the other parameters of the lattice. As in rank 3, a rank 4 PGL has an association scheme on its points. Explicit expressions are given for the eigenvalues and multiplicities. These are used to search for feasible parameter sets.
Show less  Date Issued
 1984, 1984
 PURL
 http://purl.flvc.org/fcla/dt/40603
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 PISOT SEQUENCES AND PISOTVIJAYARAGHAVAN NUMBERS.
 Creator
 DELEON, MORRIS JACK., The Pennsylvania State University
 Date Issued
 1968, 1968
 PURL
 http://purl.flvc.org/fcla/dt/40325
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 Reduced path systems and superedgegraceful trees.
 Creator
 Gottipati, Chenchu B., Locke, Stephen C., Graduate College
 Date Issued
 20130412
 PURL
 http://purl.flvc.org/fcla/dt/3361301
 Subject Headings
 Mathematics, Path analysis
 Format
 Document (PDF)
 Title
 SOME PROPERTIES OF DIVISIBILITY IN FIELDS AND INTEGRAL DOMAINS.
 Creator
 BREWER, JAMES WILLIAM., The Florida State University
 Date Issued
 1968, 1968
 PURL
 http://purl.flvc.org/fcla/dt/40315
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 SOME RESULTS IN COMBINATORIAL MATRIX THEORY.
 Creator
 Levow, Roy B., University of Pennsylvania
 Date Issued
 1969, 1969
 PURL
 http://purl.flvc.org/fcla/dt/40425
 Subject Headings
 Mathematics
 Format
 Document (PDF)