Dr. Pace Nielsen
Associate Professor
Brigham Young University

Publications

 

40. Dinesh Khurana, T. Y. Lam, and Pace P. Nielsen: Exchange elements in rings, and the equation XA-BX=I. Trans. Amer. Math. Soc. 369(1):495-516, 2017. Preprint version: pdf. Published version: DOI.

 

39. Pace P. Nielsen: The behavior of ascending chain conditions on submodules of bounded finite generation in direct sums. Israel J. Math. 215(1):339-347, 2016. Preprint version: pdf. Published version: DOI.

 

38. Dinesh Khurana, T. Y. Lam, and Pace P. Nielsen: Exchange rings, exchange equations, and lifting properties. Internat. J. of Alg. and Comput. 26(6):1177-1198, 2016. Preprint version: pdf. Published version: DOI.

 

37. George M. Bergman and Pace P. Nielsen: On Vaughan Pratt's crossword problem. J. London Math. Soc. 93(3):825-845, 2016. Preprint version: pdf. Published version: DOI.

 

36. Alexander J. Diesl, Samuel J. Dittmer, and Pace P. Nielsen: Idempotent lifting and ring extensions. J. Algebra Appl. 15(6):1650112 (16 pages), 2016. Preprint version: pdf. Published version: DOI.

 

35. Victor P. Camillo and Pace P. Nielsen: Half-orthogonal sets of idempotents. Trans. Amer. Math. Soc. 368(2):965-987, 2016. Preprint version: pdf. Published version: DOI.

 

34. Ryszard Mazurek, Pace P. Nielsen, and Michał Ziembowski: Commuting idempotents, square-free modules, and the exchange property. J. Algebra 444:52-80, 2015. Preprint version: pdf. Published version: DOI.

 

33. Pace P. Nielsen: Odd perfect numbers, Diophantine equations, and upper bounds. Math. Comp. 84(295):2549-2567, 2015. Preprint version: pdf. Published version: DOI.

(Here are the files demonstrating the results of the above paper: OPN Mathematica files)

 

32. Dinesh Khurana, T. Y. Lam, and Pace P. Nielsen: Two-sided properties of elements in exchange rings. Algebr. Represent. Theory 18(4):931-940, 2015. Preprint version: pdf. Published version: DOI.

 

31. Pace P. Nielsen, and Michał Ziembowski: Derivations and bounded nilpotence index. Internat. J. Algebra Comput. 25(3):433-438, 2015. Preprint version: pdf. Published version: DOI. Errata: errata.

 

30. Dinesh Khurana, T. Y. Lam, Pace P. Nielsen, and Yiqiang Zhou: Uniquely clean elements in rings. Comm. Alg. 43(5):1742-1751, 2015. Preprint version: pdf. Published version: DOI.

 

29. Ryszard Mazurek, Pace P. Nielsen, and Michał Ziembowski: The upper nilradical and Jacobson radical of semigroup graded rings. J. Pure Appl. Algebra 219(4):1082-1094, 2015. Preprint version: pdf. Published version: DOI.

 

28. DHJ Polymath: Variants of the Selberg sieve, and bounded intervals containing many primes. Research in the Mathematical Sciences 1:12, 2014. Definitive version: pdf. Published version: DOI.

 

27. Chan Yong Hong, Nam Kyun Kim, and Pace P. Nielsen: Radicals in skew polynomial and skew Laurent polynomial rings. J. Pure Appl. Algebra 218(10):1916-1931, 2014. Preprint version: pdf. Published version: DOI.

 

26. Anjana Khurana, Dinesh Khurana, and Pace P. Nielsen: Sums of units in self-injective rings. J. Algebra Appl. 13(6):1450020 (7 pages), 2014. Preprint version: pdf. Published version: DOI.

 

25. Samuel J. Dittmer, Dinesh Khurana, and Pace P. Nielsen: On a question of Hartwig and Luh. Bull. Aust. Math. Soc. 89:271-278, 2014. Definitive version: pdf. Published version: DOI.

 

24. T. Y. Lam and Pace P. Nielsen: Jacobson's lemma for Drazin inverses. Contemporary Mathematics 609:185-195, 2014. Preprint version: pdf. Published version: DOI.

 

23. Victor Camillo, Thomas J. Dorsey, and Pace P. Nielsen: Dedekind-finite strongly clean rings. Comm. Alg. 42(4):1619-1629, 2014. Preprint version: pdf. Published version: DOI.

 

22. T. Y. Lam and Pace P. Nielsen: Inner inverses and inner annihilators in rings. J. Algebra 397:91-110, 2014. Preprint version: pdf. Published version: DOI.

 

21. Pace P. Nielsen: Simplifying Smoktunowicz's extraordinary example. Comm. Algebra 41(11):4339-4350, 2013. Preprint version: pdf. Published version: DOI.

 

20. Alexander J. Diesl, Chan Yong Hong, Nam Kyun Kim, and Pace P. Nielsen: Properties which do not pass to classical rings of quotients. J. Algebra 379:208-222, 2013. Preprint version: pdf. Published version: DOI.

 

19. Pace P. Nielsen: Bootstrapping the bounded nilradical. J. Pure Appl. Algebra 217(9):1711-1715, 2013. Preprint version: pdf. Published version: DOI.

 

18. Chan Yong Hong, Nam Kyun Kim, Yang Lee, and Pace P. Nielsen: On σ-nil ideals of bounded index of σ-nilpotence. J. Algebra 371:492-509, 2012. Preprint version: pdf. Published version: DOI.

 

17. S. Adam Fletcher, Pace P. Nielsen, and Pascal Ochem: Sieve methods for odd perfect numbers. Math. Comp. 81(279):1753-1776, 2012. Preprint version: pdf. Published version: DOI.

(Here are the data files demonstrating the results of the above paper: OPN chains)

 

16. David A. Cardon and Pace P. Nielsen: Nonnegative minors of minor matrices. Linear Algebra Appl. 436(7):2187-2200, 2012. Preprint version: pdf. Published version: DOI.

 

15. Victor Camillo and Pace P. Nielsen: On a theorem of Camps and Dicks. Advances in ring theory (Trends Math.), 83-84, Birkhauser/Springer Basel AG, Basel, 2010. Preprint version: pdf.

 

14. Victor Camillo, Chan Yong Hong, Nam Kyun Kim, Yang Lee, and Pace P. Nielsen: Nilpotent ideals in polynomial and power series rings. Proc. Amer. Math. Soc. 138(5):1607-1619, 2010. Preprint version: pdf, errata. Published version: DOI.

 

13. Pace P. Nielsen: Square-free modules with the exchange property. J. Algebra 323(7):1993-2001, 2010. Preprint version: pdf. Published version: DOI.

 

12. Chan Yong Hong, Nam Kyun Kim, Yang Lee, and Pace P. Nielsen: The minimal prime spectrum of rings with annihilator conditions. J. Pure Appl. Algebra 213(7):1478-1488, 2009. Preprint version: pdf. Published version: DOI.

 

11. Pace P. Nielsen: A covering system whose smallest modulus is 40. J. Number Theory 129:640-666, 2009. Preprint version: pdf. Published version: DOI.

 

10. Victor Camillo and Pace P. Nielsen: McCoy rings and zero-divisors. J. Pure Appl. Algebra 212(3):599-615, 2008. Preprint version: pdf. Published version: DOI.

 

9. Victor Camillo, Ivo Herzog, and Pace P. Nielsen: Non-self-injective injective hulls with compatible multiplication. J. Algebra 314(1):471-478, 2007. Preprint version: pdf. Published version: DOI.

 

8. Pace P. Nielsen: Odd perfect numbers have at least nine distinct prime factors. Math. Comp. 76(260):2109-2126, 2007. Preprint version: pdf. Published version: DOI.

(Here are compressed copies of the printouts demonstrating the results of the above paper: First Result and Second Result)

 

7. Pace P. Nielsen: Row and column finite matrices. Proc. Amer. Math. Soc. 135(9):2689-2697, 2007. Preprint version: pdf. Published version: DOI.

 

6. Pace P. Nielsen: Countable exchange and full exchange rings. Comm. Algebra 35(1):3-23, 2007. Preprint version: pdf. Published version: DOI.

 

5. Pace P. Nielsen: The exchange property for modules and rings. Ph.D. thesis, University of California, Berkeley, May 2006. Published version: pdf, errata.

 

4. Pace P. Nielsen: Semi-commutativity and the McCoy condition. J. Algebra 298(1):134-141, 2006. Preprint version: pdf. Published version: DOI.

 

3. Pace P. Nielsen: Abelian exchange modules. Comm. Algebra 33(4):1107-1118, 2005. Preprint version: pdf. Published version: DOI.

 

2. Pace P. Nielsen: An upper bound for odd perfect numbers. Integers 3 (2003), A14, 9 pp. Preprint version: pdf. Published version: http://www.integers-ejcnt.org/vol3.html

 

1. David A. Cardon and Pace P. Nielsen: Convolution operators and entire functions with simple zeros. Number theory for the millennium, I (Urbana, IL, 2000), 153-181, A K Peters, Natick, MA, 2002. Preprint version: pdf