Books
2.
Pace P. Nielsen:
A Journey Through Formal Mathematics.
Version 1.04: pdf. (Physical copies can be purchased at lulu.com.)
1.
Darrin Doud and Pace P. Nielsen:
A Transition to Advanced Mathematics.
Version 1.03: pdf. (Physical copies can be purchased at lulu.com.)
Articles
60.
Dinesh Khurana, Xavier Mary, and Pace P. Nielsen:
Idempotent chains and bounded generation of SL2.
J. Pure Appl. Algebra 227(12):107427 (14 pages), 2023.
Preprint version: pdf.
Published version: DOI Errata: errata.
59.
Dinesh Khurana and Pace P. Nielsen:
Periodic elements and lifting connections.
J. Pure Appl. Algebra 227(11):107421 (9 pages), 2023.
Preprint version: pdf.
Published version: DOI
58.
Xavier Mary and Pace P. Nielsen:
IC rings and transitivity of perspectivity.
J. Algebra Appl. 21(8):2250151 (8 pages), 2022.
Preprint version: pdf.
Published version: DOI
57.
Cody S. Hansen and Pace P. Nielsen:
Prime factors of Φ3(x) of the same form.
Integers 22, A71, 9 pp., 2022.
Published version: pdf.
56.
Thomas L. Draper, Pace P. Nielsen, and Janez Šter:
Nilpotent polynomials and nilpotent coefficients.
J. Algebra 602:405-440, 2022.
Preprint version: pdf.
Published version: DOI
55.
BYU Computational Number Theory Group:
Odd, spoof perfect factorizations.
J. Number Theory 234:31-47, 2022.
Preprint version: pdf.
Published version: DOI
54.
Dinesh Khurana and Pace P. Nielsen:
Transitivity of perspectivity.
Algebr. Represent. Theory 25(1):281-287, 2022.
Preprint version: pdf.
Published version: DOI
53.
Pace P. Nielsen:
Definitional schemes for primitive recursive and computable functions.
Computability 11(1):1-8, 2022.
Preprint version: pdf.
Published version: DOI
52.
Dinesh Khurana and Pace P. Nielsen:
Perspectivity and von Neumann regularity.
Comm. Alg. 49(12):5483-5499, 2021.
Preprint version: pdf.
Published version: DOI
51.
Dinesh Khurana, T. Y. Lam, Pace P. Nielsen, and Janez Šter:
Special clean elements in rings.
J. Algebra Appl. 19(11):2050208 (27 pages), 2020.
Preprint version: pdf.
Published version: DOI
50.
Jongwook Baeck, Nam Kyun Kim, Yang Lee, and Pace P. Nielsen:
Zero-divisor placement, a condition of Camillo, and the McCoy property.
J. Pure Appl. Algebra 224(12):106432 (14 pages), 2020.
Preprint version: pdf.
Published version: DOI
49.
Robert D. Hough and Pace P. Nielsen:
Covering systems with restricted divisibility.
Duke Math. J. 168(17):3261-3295, 2019.
Preprint version: pdf.
Published version: DOI
48.
Anjana Khurana, Dinesh Khurana, and Pace P. Nielsen:
Symmetries in idempotent factorizations.
J. Algebra Appl. 18(5):1950084 (10 pages), 2019.
Preprint version: pdf.
Published version: DOI. Errata: errata.
47.
Chris J. Conidis, Pace P. Nielsen, and Vandy Tombs:
Transfinitely valued Euclidean domains have arbitrary indecomposable order type.
Comm. Alg. 47(3):1105-1113, 2019.
Preprint version: pdf.
Published version: DOI.
46.
T. Y. Lam and Pace P. Nielsen:
Jacobson pairs and Bott-Duffin decompositions in rings.
Rings, Modules and Codes, Contemporary Mathematics Series 727:249-267, 2019.
Preprint version: pdf.
Published version: DOI.
45.
D.H.J. Polymath (Tobias Fritz, Siddhartha Gadgil, Apoorva Khare, Pace P. Nielsen, Lior Silberman and Terence Tao):
Homogeneous length functions on groups.
Algebra Number Theory 12(7):1773-1786, 2018.
Published version: DOI.
44.
Chan Yong Hong, Nam Kyun Kim, Blake W. Madill, Pace P. Nielsen, and Michał Ziembowski:
Homogeneous nilradicals over semigroup graded rings.
J. Pure Appl. Algebra 222(7):1513-1528, 2018.
Preprint version: pdf.
Published version: DOI.
43.
Dinesh Khurana, T. Y. Lam, and Pace P. Nielsen:
An ensemble of idempotent lifting hypotheses.
J. Pure Appl. Algebra 222(6):1489-1511, 2018.
Preprint version: pdf.
Published version: DOI.
42.
Pace P. Nielsen and Janez Šter:
Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings.
Trans. Amer. Math. Soc. 370(3):1759-1782, 2018.
Preprint version: pdf.
Published version: DOI.
41.
Chan Yong Hong, Nam Kyun Kim, Yang Lee, and Pace P. Nielsen:
Amitsur's property for skew polynomials of derivation type.
Rocky Mountain J. Math. 47(7):2197-2218, 2017.
Preprint version: pdf.
Published version: DOI.
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. Errata: errata.
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. Errata: errata.
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. Errata: errata.
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. Errata: errata.
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, A14, 9 pp., 2003. 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
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