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.

 

Research Articles

 

 

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 Universitł 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 Prčfer 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 Prčfer domains, Communications in Algebra 27 (1999), pp. 4433-4458.

 

43.     Prčfer domains and pure submodules of direct sums of ideals, Mathematika, 46 (1999), 425-432.

 

44.     Composition series of modules over Prčfer domains, Proceedings of the American Mathematical Society 127 (1999), pp. 1917-1921.

 

45.     Globalizing local properties of Prčfer 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.