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W. Keith Nicholson

photograph of W. Keith Nicholson

Job Title:

  • Professor

Phone:

  • +1 (403) 220-3954

Office:

  • MS 314

Email:

Web site:

Degrees:

Office Hours:

MTWThFSSu
12p‑1p

Bars:

  • Bars

Research Interests:

  • Noncommutative rings, especially classes of exchange rings
  • Study of classes of semiperfect min-injective rings, with applications to the Faith conjecture and other questions
  • Study of clean rings and their relationship to unit regular and stable rings
  • Morphic rings and modules
  • Reflexivity of direct sums of modules over finite dimensional algebras

Masters Students:

Teaching:

Past Courses:

  • MATH211 - Linear Methods I
  • MATH221 - LINEAR ALGEBRA FOR SCIENCE & ENGG
  • MATH311 - LINEAR METHODS II
  • PMAT315 - ABSTRACT ALGEBRA
  • PMAT431 - Groups, Rings And Fields
  • PMAT621 - RESEARCH SEMINAR
  • PMAT685 - Topics In Algebra
Representative Publications:
Book
Nicholson, W. Keith. Linear Algebra with Applications (6th Edition) McGraw Hill Ryerson (2009): 566
Gilbert, William J. and Nicholson, W. Keith. Modern algebra with applications , Wiley-Interscience [John Wiley \& Sons] (2004): xviii+330
Nicholson, W. Keith and Yousif, Mohammed. Quasi-Frobenius Rings 158, Cambridge University Press (2003): xviii+307
Nicholson, W. Keith. Introduction to abstract algebra , John Wiley \& Sons Inc. (1999): xx+599
Journal Paper
Nicholson, W. Keith and Campos, E. . "Rings with the dual of the isomorphism theorem" Journal of Algebra 271.1 (2004): 391-406
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
Nicholson, W. Keith and Campos, E. . "Principal rings with the dual of the isomorphism theorem" Glasgow Mathematical Journal 46.1 (2004): 181-191
Nicholson, W. Keith and Yousif, Mohammed. "On quasi-{F}robenius rings" , (2003): xviii+307
Nicholson, W. Keith, Park, Jae and Yousif, Mohammed. "On simple-injective rings" Algebra Colloquium 9.3 (2002): 259-264
Nicholson, W. Keith and Yousif, Mohammed. "Weakly continuous and {C}2-rings" Communications in Algebra 29.6 (2001): 2429-2446
Nicholson, W. Keith and Yousif, Mohammed. "F{P}-rings" Communications in Algebra 29.1 (2001): 415-425
Nicholson, W. Keith and Yousif, Mohammed. "C2-rings and the {FGF}-conjecture" , 273 (2001): 245-251
Han, Juncheol and Nicholson, W. Keith. "Extensions of clean rings" Communications in Algebra 29.6 (2001): 2589-2595
Nicholson, W. Keith and Yousif, Mohammed. "On finitely embedded rings" Communications in Algebra 28.11 (2000): 5311-5315
Nicholson, W. Keith, Park, Jae and Yousif, Mohammed. "Extensions of simple-injective rings" Communications in Algebra 28.10 (2000): 4665-4675
Camillo, V. , Nicholson, W. Keith and Yousif, Mohammed. "Ikeda-{N}akayama rings" Journal of Algebra 226.2 (2000): 1001-1010
Ara, Pere , Nicholson, W. Keith and Yousif, Mohammed. "A look at the {F}aith conjecture" Glasgow Mathematical Journal 42.3 (2000): 391-404
Nicholson, W. Keith. "Strongly clean rings and {F}itting's lemma" Communications in Algebra 27.8 (1999): 3583-3592
Han, Juncheol and Nicholson, W. Keith. "Notes on clean rings" (1999): 23-32
Nicholson, W. Keith, Park, J. K. and Yousif, Mohammed. "Principally quasi-injective modules" Communications in Algebra 27.4 (1999): 1683-1693
Nicholson, W. Keith and Yousif, Mohammed. "On dual rings" New Zealand Journal of Mathematics 28.1 (1999): 65-70
Nicholson, W. Keith and Varadarajan, Kalathoor . "Countable linear transformations are clean" Proc. Amer. Math. Soc. 126.1 (1998): 61-64
Nicholson, W. Keith and Yousif, Mohammed. "Corrigendum: ``{A}nnihilators and the {CS}-condition''" Glasgow Mathematical Journal 40.3 (1998): 475-476
Nicholson, W. Keith and Yousif, Mohammed. "Annihilators and the {CS}-condition" Glasgow Mathematical Journal 40.2 (1998): 213-222
Nicholson, W. Keith. "On exchange rings" Communications in Algebra 25.6 (1997): 1917-1918
Nicholson, W. Keith. "Very semisimple modules" The American Mathematical Monthly 104.2 (1997): 159-162
Nicholson, W. Keith and Yousif, Mohammed. "Mininjective rings" Journal of Algebra 187.2 (1997): 548-578
Fuller, K. R., Nicholson, W. Keith and Watters, J. F. "On {$k$}-reflexive representations of algebras" Proc. Amer. Math. Soc. 125.1 (1997): 47-50
Nicholson, W. Keith and Yousif, Mohammed. "On perfect simple-injective rings" Proc. Amer. Math. Soc. 125.4 (1997): 979-985
Fuller, K. R., Nicholson, W. Keith and Watters, J. F. "Direct sums of reflexive modules" Linear Algebra and its Applications 239 (1996): 201-214
Nicholson, W. Keith. "An elementary proof of a characterization of semiperfect rings" New Zealand Journal of Mathematics 25.2 (1996): 195-197
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
Nicholson, W. Keith and Yousif, Mohammed. "Principally injective rings" Journal of Algebra 174.1 (1995): 77-93
Fuller, K. R., Nicholson, W. Keith and Watters, J. F. "Algebras whose projective modules are reflexive" Journal of Pure and Applied Algebra 98.2 (1995): 135-150
Nicholson, W. Keith and Varadarajan, Kalathoor . "Endomorphisms and global dimension" Acta Mathematica Hungarica 67.1-2 (1995): 93-96
Nicholson, W. Keith and Yousif, Mohammed. "On completely principally injective rings" Bulletin of the Australian Mathematical Society 49.3 (1994): 513-518
Nicholson, W. Keith and Yousif, Mohammed. "Continuous rings with chain conditions" Journal of Pure and Applied Algebra 97.3 (1994): 325-332
Nicholson, W. Keith and Yousif, Mohammed. "On quasi-continuous rings" Proc. Amer. Math. Soc. 120.4 (1994): 1049-1051
Nicholson, W. Keith. "On {PP}-endomorphism rings" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 36.2 (1993): 227-230
Nicholson, W. Keith. "On {PP}-rings" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 27.2 (1993): 85-88
Nicholson, W. Keith. "A short proof of the {W}edderburn-{A}rtin theorem" New Zealand Journal of Mathematics 22.1 (1993): 83-86
Nicholson, W. Keith and Watters, J. F. "Classes of simple modules and triangular rings" Communications in Algebra 20.1 (1992): 141-153
Fuller, K. R., Nicholson, W. Keith and Watters, J. F. "Universally reflexive algebras" Linear Algebra and its Applications 157 (1991): 195-201
Nicholson, W. Keith. "On {F}aith's correspondence theorem" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 21.1 (1990): 31-34
Fraser, J. A. and Nicholson, W. Keith. "Reduced {PP}-rings" Mathematica Japonica 34.5 (1989): 715-725
Fuller, K. R., Nicholson, W. Keith and Watters, J. F. "Reflexive bimodules" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 41.4 (1989): 592-611
Nicholson, W. Keith and Watters, J. F. "Exact modules" Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 51.5 (1988): 412-418
Nicholson, W. Keith. "The dual of a theorem of {G}oldman" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 19.3 (1988): 235-239
Nicholson, W. Keith and Watters, J. F. "Morita context functors" Mathematical Proceedings of the Cambridge Philosophical Society 103.3 (1988): 399-408
Nicholson, W. Keith and Watters, J. F. "Rings with projective socle" Proc. Amer. Math. Soc. 102.3 (1988): 443-450
Nicholson, W. Keith and Watters, J. F. "Normal radicals and normal classes of modules" Glasgow Mathematical Journal 30.1 (1988): 97-100
Nicholson, W. Keith and Sarath, B. . "Rings with a largest linear topology" Communications in Algebra 13.4 (1985): 769-780
Nicholson, W. Keith and Watters, J. F. "Central closures and {M}orita contexts" Communications in Algebra 12.1-2 (1984): 103-123
Nicholson, W. Keith and Watters, J. F. "On tensor products and extended centroids" Proc. Amer. Math. Soc. 88.2 (1983): 215-217
Nicholson, W. Keith and Watters, J. F. "Normal classes of rings and tensor products" Communications in Algebra 9.3 (1981): 299-311
Desale, G. and Nicholson, W. Keith. "Endoprimitive rings" Journal of Algebra 70.2 (1981): 548-560
Nicholson, W. Keith and Watters, J. F. "Normal classes of prime rings determined by modules" Proc. Amer. Math. Soc. 83.1 (1981): 27-30
Nicholson, W. Keith, Watters, J. F. and Zelmanowitz, J. M. "On extensions of weakly primitive rings" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 32.4 (1980): 937-944
Nicholson, W. Keith and Yaqub, Adil . "A commutativity theorem" Algebra Universalis 10.2 (1980): 260-263
Nicholson, W. Keith and Watters, J. F. "The strongly prime radical" Proc. Amer. Math. Soc. 76.2 (1979): 235-240
Nicholson, W. Keith and Yaqub, Adil . "A commutativity theorem for rings and groups" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 22.4 (1979): 419-423
Nicholson, W. Keith and Watters, J. F. "Normal radicals and normal classes of rings" Journal of Algebra 59.1 (1979): 5-15
Nicholson, W. Keith. "Lifting idempotents and exchange rings" Transactions of the American Mathematical Society 229 (1977): 269-278
Nicholson, W. Keith and Springer, H. J. "Commutativity of rings with abelian or solvable units" Proc. Amer. Math. Soc. 56 (1976): 59-62
Nicholson, W. Keith. "Semiregular modules and rings" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 28.5 (1976): 1105-1120
Nicholson, W. Keith and Springer, H. J. "Local rings with elementary {A}belian units" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 19.2 (1976): 205-208
Nicholson, W. Keith. "{$I$}-rings" Transactions of the American Mathematical Society 207 (1975): 361-373
Nicholson, W. Keith. "On semiperfect modules" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 18.1 (1975): 77-80
Nicholson, W. Keith. "Semiperfect rings with abelian adjoint group" Pacific Journal of Mathematics 54 (1974): 201-207
Nicholson, W. Keith. "Semiperfect rings with abelian group of units" Pacific Journal of Mathematics 49 (1973): 191-198
Nicholson, W. Keith. "Rings whose elements are quasi-regular or regular" Aequationes Mathematicae 9 (1973): 64-70
Nicholson, W. Keith. "Local group rings" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 15 (1972): 137-138
Preprint
Nicholson, W. Keith. "Lifting Idempotents and Exchange Rings" Research Paper.298 (1975): 1 - 18

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