Bruce
Olberding
Department
of Mathematical Sciences
New Mexico
State University
Las Cruces,
NM 88003-8001
My research interests include commutative
ring theory, valuation theory and module theory. Some recent projects include work on the
Zariski-Riemann space of a field, intersections of
valuation overrings of two-dimensional Noetherian domains; constructing bad
Noetherian rings from derivations; stable rings; analytically ramified
one-dimensional local Noetherian domains; ideal decompositions in commutative
rings; Prufer overrings of Noetherian domains; and holomorphy
rings in function fields.
1.
Affine
schemes and topological closures in the Zariski-Riemann
space of valuation rings, preprint.
2.
One-dimensional
bad Noetherian domains, Transactions of the American
Mathematical Society, to appear.
3.
Generic formal fibers and
analytically ramified stable rings, Nagoya Journal of Mathematics, to appear, arXiv:1208.2913v1
4.
Integrally closed
rings in birational extensions of two-dimensional regular
local rings,
with Francesca Tartarone, Mathematical Proceedings of
the Cambridge Philosophical Society, to appear.
5.
A counterpart to Nagata
idealization,
Journal of Algebra 365 (2012), 199–221.
6.
Noetherian rings without finite normalization, in Progress in commutative
algebra 2, 171–203,
Walter de Gruyter,
Berlin, 2012.
7.
Noetherian
spaces of integrally closed rings with an application to intersections of
valuation rings,
Communications in Algebra,
38 (2010), no. 9, 3318-3332.
8.
Intersections
of valuation overrings of two-dimensional Noetherian domains,
Commutative algebra—Noetherian and non-Noetherian perspectives, 335–361, Springer,
New York, 2011.
9.
On Matlis domains and Prufer
sections of Noetherian domains, in Commutative Algebra and its
applications, 321-332, Walter de Gruyter, Berlin, 2009.
10.
Factorization into prime and invertible
ideals II, Journal
of the London Mathematical Society, Journal
of the London Mathematical Society (2) 80 (2009), no. 1, 155-170.
11.
Characterizations
and construction of h-local domains, in Models,
modules and abelian groups, 385-406, Walter de Gruyter, Berlin,
2008.
12.
Integrally closed overrings of two-dimensional Noetherian
domains representable by Noetherian spaces of
valuation rings, Journal
of Pure and Applied Algebra 212 (2008) 1791-1821.
13.
Pure submodules
of completely decomposable modules, with H. P. Goeters, Houston
Journal of Mathematics 34 (2008), no. 2, 373-382.
14.
Irredundant intersections of
valuation overrings of two-dimensional Noetherian domains, Journal of Algebra 318 (2007) 834-855.
15.
Injective and colon properties
of ideals of integral domains, Forum Mathematicum 19
(2007), no. 6, 1047-1074.
16.
Holomorphy rings of function fields, in Multiplicative Ideal Theory
in Commutative Algebra, 331-348, Springer-Verlag,
2006.
17.
The minimal
number of generators of an invertible ideal, with Moshe Roitman,
in Multiplicative Ideal Theory in Commutative Algebra, 349-368, Springer-Verlag, 2006.
18.
Commutative ideal theory without
finiteness conditions: irreducibility in the quotient field, with Laszlo Fuchs and William Heinzer, in Abelian groups, rings, modules, and
homological algebra, 121-145, Lecture Notes in Pure and Applied
Mathematics, 249, Chapman & Hall/CRC, Boca
Raton, FL, 2006.
19.
Commutative
ideal theory without finiteness conditions: completely irreducible ideals with
Laszlo Fuchs and William Heinzer, Transactions of the American
Mathematical Society, 358 (2006), no. 7, 3113-3131.
20.
Unique irredundant intersections
of completely irreducible ideals, with William Heinzer, Journal
of Algebra 287 (2005), no. 2, 432-448.
21.
Ultrapowers,
valuations and completions of Noetherian domains, with Serpil
Saydam and Jay Shapiro, Journal of Pure and Applied
Algebra, 197 (2005), no. 1-3, 213-237.
22.
Prime ideals in ultraproducts of commutative rings, with Jay Shapiro, Journal of
Algebra, 285 (2005), no. 2, 768-794.
23.
Factorization
into radical ideals,
in Arithmetical properties of commutative rings and monoids,
363-377, Lecture Notes in Pure and Applied Mathematics, 241, Chapman &
Hall/CRC, Boca Raton, FL, 2005.
24.
Projective
presentations of finitely generated modules with large annihilators, with Serpil
Saydam, Communications in Algebra, 33 (2005), no. 1,
201-212.
25.
Commutative
ideal theory without finiteness conditions: primal ideals, with Laszlo Fuchs and William Heinzer, Transactions of the American Mathematical Society,
357 (2005), no. 7, 2771-2798.
26.
Maximal
prime divisors in arithmetical rings, with Laszlo Fuchs and William Heinzer,
Rings,
modules, algebras, and abelian groups, 189-203, Lecture Notes in Pure and Applied Mathematics, 236, Marcel Dekker, New York, 2004.
27.
The Krull-Schmidt
property for ideals and modules over integral domains, with H. P. Goeters,
Rocky Mountain Journal of Mathematics, 32 (2002), 1409-1429.
28.
A geometric setting for some properties
of torsion-free modules,
Rocky Mountain Journal of Mathematics, 32 (2002), 1281-1297.
29.
On the structure of stable
domains,
Communications in Algebra, 30 (2002), 877-895.
30.
Ultraproducts
of commutative rings,
with Serpil Saydam,
Commutative ring theory and applications, Lecture Notes in Pure and Applied
Mathematics 231, Marcel Dekker, 2002, 369-387.
31.
Unique decompositions into
ideals of Noetherian domains, with H. P. Goeters,
Journal of Pure and Applied Algebra, 165 (2001), 169-182.
32.
On locally isomorphic
torsion-free modules,
with H. P. Goeters, International Journal of
Commutative Rings, 1 (2001), 83-94.
33.
Stability, duality, 2-generated
ideals and a canonical decomposition of modules, Rendiconti
del Seminario Matematico della Universitˆ di Padova, 106 (2001), 261-290.
34.
On the classification of stable
domains, Journal
of Algebra, 243 (2001), 177-197.
35.
Stability of ideals and its applications, in
Ideal-Theoretic Methods in Commutative Algebra, edited by I. Papick
and D.D. Anderson, Marcel Dekker, 2001.
36.
Homomorphisms
and duality for torsion-free modules, Proceedings of the AGRAM Conference, Perth, Australia,
2000, Contemporary Mathematics, 2001, 17-38.
37.
Extension of ideal-theoretic
properties of a domain to submodules of its quotient
field, with H.
P. Goeters, Journal of Algebra, 237 (2001), 14-31.
38.
Factorization into prime and
invertible ideals,
Journal of the London Mathematical Society (2), 62 (2000), 336-344.
39.
Modules of injective dimension
one over PrŸfer domains, Journal of Pure and Applied
Algebra 153 (2000), pp. 263-287.
40.
On the multiplicative properties
of submodules of the quotient field of an integral
domain, with H.
P. Goeters, Houston Journal of Mathematics 26 (2000),
pp. 241-254.
41.
Faithfulness and cancellation
over Noetherian domains, with H.P. Goeters,
Rocky Mountain Journal of Mathematics 30 (2000), pp. 185-194.
42.
Almost maximal PrŸfer domains, Communications in Algebra 27 (1999), pp. 4433-4458.
43.
PrŸfer
domains and pure submodules of direct sums of ideals, Mathematika,
46 (1999), 425-432.
44.
Composition series of modules
over PrŸfer domains, Proceedings of the American Mathematical
Society 127 (1999), pp. 1917-1921.
45.
Globalizing local properties of PrŸfer domains, Journal of Algebra 205 (1998), pp. 480-504.
46.
E-uniserial groups, with M. Dugas, Methods in Module
Theory, New York: Marcel Dekker, 1993, pp. 75-86.