W. Keith Nicholson

Professor Emeritus of Mathematics & Statistics

Department of Mathematics and Statistics

PhD

University of California at Santa Barbara, 1970

MS

Stanford University, 1966

MSc

University of Alberta, 1963

BSc

University of Alberta, 1961

Contact information

Phone

Office: 403.220.3954

Location

Office : MS314

Research and teaching

Research areas

  • Noncommutative rings, especially classes of exchange rings
  • Study of clean rings and their relationship to unit regular and stable rings
  • Morphic and quasi-morphic rings
  • Stable and unit-regular modules

Publications

Book

  • Nicholson, W. Keith. Linear Algebra with Applications, Sixth Edition McGraw Hill Ryerson, 2009. 566. Print.
  • Gilbert, William J. and Nicholson, W. Keith. Modern algebra with applications , Wiley-Interscience [John Wiley \& Sons], 2004. xviii+330. Print.
  • Nicholson, W. Keith and Yousif, Mohammed. Quasi-Frobenius Rings 158. Cambridge University Press, 2003. xviii+307. Print.
  • Nicholson, W. Keith. Introduction to abstract algebra , John Wiley \& Sons Inc., 1999. xx+599. Print.

Conference proceedings

  • Nicholson, W. Keith and Zhou, Y.. Clean rings: A survey 2004.
  • Nicholson, W. Keith. A survey of morphic rings and modules 2004.

Journal article

  • Nicholson, W. Keith and Camillo, V.. "On rings where left principal ideals are left principal annihilators". International Electronic Journal of Algebra 17 (2015), 199-214 17. (2014): 199-214. Print.
  • Nicholson, W. Keith and F. Aliniafeifard and Y. Li. "Morphic p-groups". J. Pure and Applied Algebra 217. (2013): 1864-1869. Print.
  • Nicholson, W. Keith. "Semiprime left quasi-morphic rings". J. Algebra and its Applications 12. (2013). Print.
  • Nicholson, W. Keith and M. Alkan and C. Ozcan. "Strong lifting splits". J. Pure and Applied Algebra 215. (2011): 1879-1888. Print.
  • Nicholson, W. Keith and H. Chen. "On regular modules". Bull. Australian Math. Soc. 84. (2011): 280-287. Print.
  • Nicholson, W. Keith and Y. Zhou. "Annihilator-small right ideals". Algebra Colloquium 18. (2011): 785-800. Print.
  • Li, Y. and Nicholson, W. Keith. "Ehrlich's theorem for groups". Bulletin of the Australian Mathematical Society 81. (2010): 304-309. Print.
  • Li, Y., Nicholson, W. Keith and Zan, L.. "Morphic groups". Journal of Pure and Applied Algebra 214. (2010): 1827-1834. Print.
  • Alkan, M., Nicholson, W. Keith and Ozcan, A.C.. "A generalization of projective covers". Journal of Algebra 319. (2008): 4947-4960. Print.
  • Camillo, V.P., Nicholson, W. Keith and Wang, Z.. "Left quasi-morphic rings". Journal of Algebra and its Applications 7. (2008): 725-733. Print.
  • Nicholson, W. Keith and Diesl, A.J.. "Some examples concerning left morphic elements in corner rings". Journal of Algebra 315. (2007): 745-750. Print.
  • Camillo, V.P. and Nicholson, W. Keith. "Quasi-morphic rings". Journal of Algebra and its Applications 6. (2007): 789-799. Print.
  • Nicholson, W. Keith and Y. Zhou. "Semiregular morphisms". Comm. in Algebra 34. (2006): 219-233. Print.
  • Camillo, V.P., Khurana, D., Lam, T.Y., Nicholson, W. Keith and Zhou, Y.. "Continuous modules are clean". Journal of Algebra 304. (2006): 94-111. Print.
  • Chen, J., Nicholson, W. Keith and Zhou, Y.. "Group rings in which every element is uniquely the sum of a unit and an idempotent". Journal of Algebra 306. (2006): 453-460. Print.
  • Nicholson, W. Keith and Sanchez Campos, E.. "Morphic modules". Communications in Algebra 33. (2005): 2629-2647. Print.
  • Nicholson, W. Keith and Zhou, Y.. "Endomorphisms that are the sum of a unit and a root of a fixed polynomial". Canadian Mathematical Bulletin 49.2 (2005): 265-269. Print.
  • Nicholson, W. Keith and Zhou, Y.. "Strong lifting". Journal of Algebra 285. (2005): 795-818. Print.
  • Nicholson, W. Keith and Zhou, Y.. "Clean general rings". Journal of Algebra 291. (2005): 297-311. Print.
  • Nicholson, W. Keith, Varadarajan, K. and Zhou, Y.. "Clean endomorphism rings". Archiv der Mathematik 83. (2004): 340-343. Print.
  • Nicholson, W. Keith and Campos, E.. "Principal rings with the dual of the isomorphism theorem". Glasgow Mathematical Journal 46.1 (2004): 181-191. Print.
  • Nicholson, W. Keith and Zhou, Y.. "Rings in which elements are uniquely the sum of an idempotent and a unit". Glasgow Mathematical Journal 46. (2004): 227-236. Print.
  • Nicholson, W. Keith and Sanchez Campos, E.. "Rings with the dual of the isomorphism theorem". Journal of Algebra 271. (2004): 391-406. Print.
  • Nicholson, W. Keith and Zhou, Y.. "Clean rings: A survey". Advances in Ring Theory, Proceedings of the Fourth China-Japan-Korea International Conference, World Scientific, 167-180, (2004): 181-198. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "On quasi-Frobenius rings". , , Cambridge University Press, (2003): xviii+307. Print.
  • Nicholson, W. Keith, Park, Jae, Yousif, M.F. and Yousif, Mohammed. "On simple-injective rings". Algebra Colloquium 9.3 Cambridge University Press, (2002): 259-264. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "Weakly continuous and C2-rings". Communications in Algebra 29. (2001): 2429-2446. Print.
  • Han, Juncheol and Nicholson, W. Keith. "Extensions of clean rings". Communications in Algebra 29.6 Cambridge University Press, (2001): 2589-2595. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "FP-rings". Communications in Algebra 29. Cambridge University Press, (2001): 415-425. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "C2-rings and the FGF-conjecture". , 273. Amer. Math. Soc., (2001): 245-251. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "On finitely embedded rings". Communications in Algebra 28.11 Cambridge University Press, (2000): 5311-5315. Print.
  • Park, Jae, Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "On extensions of simple-injective rings". Communications in Algebra 28.10 Cambridge University Press, (2000): 4665-4675. Print.
  • Ara, Pere, Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "A look at the Faith conjecture". Glasgow Mathematical Journal 42. Cambridge University Press, (2000): 391-404. Print.
  • Camillo, V., Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "Ikeda-Nakayama rings". Journal of Algebra 226. (2000): 1001-1010. Print.
  • Han, Juncheol and Nicholson, W. Keith. "Notes on clean rings". , (1999): 23-32. Print.
  • Nicholson, W. Keith, Park, J. K., Yousif, M.F. and Yousif, Mohammed. "Principally quasi-injective modules". Communications in Algebra 27.4 John Wiley & Sons Inc., (1999): 1683-1693. Print.
  • Nicholson, W. Keith. "Strongly clean rings and Fitting's lemma". Communications in Algebra 27. (1999): 3583-3592. Print.
  • Nicholson, W. Keith and Yousif, Mohammed. "On dual rings". New Zealand Journal of Mathematics 28.1 John Wiley & Sons Inc., (1999): 65-70. Print.
  • Nicholson, W. Keith and Varadarajan, Kalathoor. "Countable linear transformations are clean". Proc. Amer. Math. Soc. 126.1 (1998): 61-64. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "Annihilators and the CS-condition". Glasgow Mathematical Journal 40. John Wiley & Sons Inc., (1998): 213-222. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "Corrigendum: ``Annihilators and the CS-condition''". Glasgow Mathematical Journal 40.3 John Wiley & Sons Inc., (1998): 475-476. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "On perfect simple-injective rings". Proc. Amer. Math. Soc. 125.4 (1997): 979-985. Print.
  • Fuller, K. R., Nicholson, W. Keith and Watters, J. F.. "On k-reflexive representations of algebras". Proc. Amer. Math. Soc. 125.1 John Wiley & Sons Inc., (1997): 47-50. Print.
  • Nicholson, W. Keith. "On exchange rings". Communications in Algebra 25.6 John Wiley & Sons Inc., (1997): 1917-1918. Print.
  • Nicholson, W. Keith. "Very semisimple modules". The American Mathematical Monthly 104.2 John Wiley & Sons Inc., (1997): 159-162. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "Mininjective rings". Journal of Algebra 187.2 John Wiley & Sons Inc., (1997): 548-578. Print.
  • Fuller, K. R., Nicholson, W. Keith and Watters, J. F.. "Direct sums of reflexive modules". Linear Algebra and its Applications 239. John Wiley & Sons Inc., (1996): 201-214. Print.
  • Nicholson, W. Keith. "An elementary proof of a characterization of semiperfect rings". New Zealand Journal of Mathematics 25.2 John Wiley & Sons Inc., (1996): 195-197. Print.
  • Nicholson, W. Keith and Yousif, M.F.. "On a theorem of Camillo". Communications in Algebra 23. (1995): 5309-5314. Print.
  • Fuller, K. R., Nicholson, W. Keith and Watters, J. F.. "Algebras whose projective modules are reflexive". Journal of Pure and Applied Algebra 98.2 John Wiley & Sons Inc., (1995): 135-150. Print.
  • Nicholson, W. Keith and Varadarajan, Kalathoor. "Endomorphisms and global dimension". Acta Mathematica Hungarica 67.1-2 (1995): 93-96. Print.
  • Nicholson, W. Keith and Varadarajan, Kalathoor. "Complement preserving operators". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 30.3 (1995): 225-232. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "Principally injective rings". Journal of Algebra 174.1 (1995): 77-93. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "On quasi-continuous rings". Proc. Amer. Math. Soc. 120.4 John Wiley & Sons Inc., (1994): 1049-1051. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "Continuous rings with chain conditions". Journal of Pure and Applied Algebra 97.3 John Wiley & Sons Inc., (1994): 325-332. Print.
  • Nicholson, W. Keith, Yousif, M.F. and Yousif, Mohammed. "On completely principally injective rings". Bulletin of the Australian Mathematical Society 49.3 John Wiley & Sons Inc., (1994): 513-518. Print.
  • Nicholson, W. Keith. "On PP-endomorphism rings". Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 36.2 John Wiley & Sons Inc., (1993): 227-230. Print.
  • Nicholson, W. Keith. "A short proof of the Wedderburn-Artin theorem". New Zealand Journal of Mathematics 22.1 John Wiley & Sons Inc., (1993): 83-86. Print.
  • Nicholson, W. Keith. "On PP-rings". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 27.2 John Wiley & Sons Inc., (1993): 85-88. Print.
  • Nicholson, W. Keith and Watters, J. F.. "Classes of simple modules and triangular rings". Communications in Algebra 20.1 John Wiley & Sons Inc., (1992): 141-153. Print.
  • Fuller, K. R., Nicholson, W. Keith and Watters, J. F.. "Universally reflexive algebras". Linear Algebra and its Applications 157. John Wiley & Sons Inc., (1991): 195-201. Print.
  • Nicholson, W. Keith. "On Faith's correspondence theorem". Periodica Mathematica Hungarica. Journal of the Janos Bolyai Mathematical Society 21.1 John Wiley & Sons Inc., (1990): 31-34. Print.
  • Fraser, J. A. and Nicholson, W. Keith. "Reduced PP-rings". Mathematica Japonica 34.5 (1989): 715-725. Print.
  • Fuller, K. R., Nicholson, W. Keith and Watters, J. F.. "Reflexive bimodules". Canadian Journal of Mathematics 41.4 (1989): 592-611. Print.
  • Nicholson, W. Keith and Watters, J. F.. "Rings with projective socle". Proc. Amer. Math. Soc. 102.3 (1988): 443-450. Print.
  • Nicholson, W. Keith and Watters, J. F.. "Normal radicals and normal classes of modules". Glasgow Mathematical Journal 30.1 (1988): 97-100. Print.
  • Nicholson, W. Keith and Watters, J. F.. "Morita context functors". Mathematical Proceedings of the Cambridge Philosophical Society 103.3 John Wiley & Sons Inc., (1988): 399-408. Print.
  • Nicholson, W. Keith and Watters, J. F.. "Exact modules". Archiv der Mathematik 51.5 (1988): 412-418. Print.
  • Nicholson, W. Keith. "The dual of a theorem of Goldman". Periodica Mathematica Hungarica. Journal of the Janos Bolyai Mathematical Society 19.3 (1988): 235-239. Print.
  • Nicholson, W. Keith and Sarath, B.. "Rings with a largest linear topology". Communications in Algebra 13.4 (1985): 769-780. Print.
  • Nicholson, W. Keith and Watters, J. F.. "Central closures and Morita contexts". Communications in Algebra 12.1-2 (1984): 103-123. Print.
  • Nicholson, W. Keith and Watters, J. F.. "On tensor products and extended centroids". Proc. Amer. Math. Soc. 88.2 (1983): 215-217. Print.
  • Nicholson, W. Keith and Watters, J. F.. "Normal classes of prime rings determined by modules". Proc. Amer. Math. Soc. 83.1 (1981): 27-30. Print.
  • Nicholson, W. Keith and Watters, J. F.. "Normal classes of rings and tensor products". Communications in Algebra 9.3 (1981): 299-311. Print.
  • Desale, G. and Nicholson, W. Keith. "Endoprimitive rings". Journal of Algebra 70.2 (1981): 548-560. Print.
  • Nicholson, W. Keith and Yaqub, Adil. "A commutativity theorem". Algebra Universalis 10.2 (1980): 260-263. Print.
  • Nicholson, W. Keith, Watters, J. F. and Zelmanowitz, J. M.. "On extensions of weakly primitive rings". Canadian Journal of Mathematics. 32.4 (1980): 937-944. Print.
  • Nicholson, W. Keith and Watters, J. F.. "The strongly prime radical". Proc. Amer. Math. Soc. 76.2 (1979): 235-240. Print.
  • Nicholson, W. Keith and Yaqub, Adil. "A commutativity theorem for rings and groups". Canadian Mathematical Bulletin 22.4 (1979): 419-423. Print.
  • Nicholson, W. Keith and Watters, J. F.. "Normal radicals and normal classes of rings". Journal of Algebra 59.1 (1979): 5-15. Print.
  • Nicholson, W. Keith. "Lifting idempotents and exchange rings". Transactions of the American Mathematical Society 229. (1977): 269-278. Print.
  • Nicholson, W. Keith and Springer, H. J.. "Commutativity of rings with abelian or solvable units". Proc. Amer. Math. Soc. 56. (1976): 59-62. Print.
  • Nicholson, W. Keith and Springer, H. J.. "Local rings with elementary Abelian units". Canadian Mathematical Bulletin 19.2 (1976): 205-208. Print.
  • Nicholson, W. Keith. "Semiregular modules and rings". Canadian Journal of Mathematics 28.5 (1976): 1105-1120. Print.
  • Nicholson, W. Keith. "I-rings". Transactions of the American Mathematical Society 207. (1975): 361-373. Print.
  • Nicholson, W. Keith. "On semiperfect modules". Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 18.1 (1975): 77-80. Print.
  • Nicholson, W. Keith. "Semiperfect rings with abelian adjoint group". Pacific Journal of Mathematics 54. (1974): 201-207. Print.
  • Nicholson, W. Keith. "Rings whose elements are quasi-regular or regular". Aequationes Mathematicae 9. (1973): 64-70. Print.
  • Nicholson, W. Keith. "Semiperfect rings with abelian group of units". Pacific Journal of Mathematics 49. (1973): 191-198. Print.
  • Nicholson, W. Keith. "Local group rings". Canadian Mathematical Bulletin 15. (1972): 137-138. Print.

Journal articles - peer reviewed

  • Nicholson, W. Keith and H. Chen. "Stable modules and a theorem of Camillo and Yu". J. Pure and Applied Algebra 218. (2014): 1431-1442. Print.

Preprint

  • Nicholson, W. Keith. "Lifting Idempotents and Exchange Rings". Research Paper.298 (1975): 1 - 18. Print.