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W. Keith Nicholson
Job Title:
- Professor
Phone:
- +1 (403) 220-3954
Office:
- MS 314
Degrees:
- 1961 - B.Sc. - University of Alberta
- 1963 - M.Sc. - University of Alberta
- 1966 - MS - Stanford University
- 1970 - Ph.D. - University of California at Santa Barbara
Office Hours:
| M | T | W | Th | F | S | Su |
|---|---|---|---|---|---|---|
| 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 Student:
- Marcus Wilson (2007)
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 | |||
| 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 (BOOK) 158, Cambridge University Press (2003): xviii+307 | |||
| Nicholson, W. Keith and Yousif, Mohammed. On quasi-{F}robenius rings , Birkh\"auser Boston (2001): 245-277 | |||
| Nicholson, W. Keith and Yousif, Mohammed. C2-rings and the {FGF}-conjecture 273, Amer. Math. Soc. (2001): 245-251 | |||
| Nicholson, W. Keith. "Introduction to abstract algebra" Communications in Algebra, , John Wiley \& Sons Inc. (1999): xx+599 | |||
| Journal Paper | |||
| 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 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, Park, Jae and Yousif, Mohammed. "On simple-injective rings" Algebra Colloquium 9.3, Cambridge University Press (2002): 259-264 | |||
| Han, Juncheol and Nicholson, W. Keith. "Extensions of clean rings" Communications in Algebra 29.6, Cambridge University Press (2001): 2589-2595 | |||
| Nicholson, W. Keith and Yousif, Mohammed. "F{P}-rings" Communications in Algebra 29.1, Cambridge University Press (2001): 415-425 | |||
| Nicholson, W. Keith and Yousif, Mohammed. "Weakly continuous and {C}2-rings" Communications in Algebra 29.6 (2001): 2429-2446 | |||
| Ara, Pere , Nicholson, W. Keith and Yousif, Mohammed. "A look at the {F}aith conjecture" Glasgow Mathematical Journal 42.3, Cambridge University Press (2000): 391-404 | |||
| Nicholson, W. Keith and Yousif, Mohammed. "On finitely embedded rings" Communications in Algebra 28.11, Cambridge University Press (2000): 5311-5315 | |||
| Nicholson, W. Keith, Park, Jae and Yousif, Mohammed. "Extensions of simple-injective rings" Communications in Algebra 28.10, Cambridge University Press (2000): 4665-4675 | |||
| Camillo, V. , Nicholson, W. Keith and Yousif, Mohammed. "Ikeda-{N}akayama rings" Journal of Algebra 226.2 (2000): 1001-1010 | |||
| Nicholson, W. Keith and Yousif, Mohammed. "On dual rings" New Zealand Journal of Mathematics 28.1, John Wiley & Sons Inc. (1999): 65-70 | |||
| Nicholson, W. Keith, Park, J. K. and Yousif, Mohammed. "Principally quasi-injective modules" Communications in Algebra 27.4, John Wiley & Sons Inc. (1999): 1683-1693 | |||
| Han, Juncheol and Nicholson, W. Keith. Notes on clean rings (1999): 23-32 | |||
| Nicholson, W. Keith. "Strongly clean rings and {F}itting's lemma" Communications in Algebra 27.8 (1999): 3583-3592 | |||
| Nicholson, W. Keith and Yousif, Mohammed. "Corrigendum: ``{A}nnihilators and the {CS}-condition''" Glasgow Mathematical Journal 40.3, John Wiley & Sons Inc. (1998): 475-476 | |||
| Nicholson, W. Keith and Yousif, Mohammed. "Annihilators and the {CS}-condition" Glasgow Mathematical Journal 40.2, John Wiley & Sons Inc. (1998): 213-222 | |||
| Nicholson, W. Keith and Varadarajan, Kalathoor . "Countable linear transformations are clean" Proc. Amer. Math. Soc. 126.1 (1998): 61-64 | |||
| Nicholson, W. Keith. "On exchange rings" Communications in Algebra 25.6, John Wiley & Sons Inc. (1997): 1917-1918 | |||
| Nicholson, W. Keith. "Very semisimple modules" The American Mathematical Monthly 104.2, John Wiley & Sons Inc. (1997): 159-162 | |||
| Nicholson, W. Keith and Yousif, Mohammed. "Mininjective rings" Journal of Algebra 187.2, John Wiley & Sons Inc. (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, John Wiley & Sons Inc. (1997): 47-50 | |||
| Nicholson, W. Keith and Yousif, Mohammed. "On perfect simple-injective rings" Proc. Amer. Math. Soc. 125.4 (1997): 979-985 | |||
| 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 | |||
| 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 | |||
| 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 | |||
| 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 | |||
| 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. "Continuous rings with chain conditions" Journal of Pure and Applied Algebra 97.3, John Wiley & Sons Inc. (1994): 325-332 | |||
| Nicholson, W. Keith and Yousif, Mohammed. "On completely principally injective rings" Bulletin of the Australian Mathematical Society 49.3, John Wiley & Sons Inc. (1994): 513-518 | |||
| Nicholson, W. Keith and Yousif, Mohammed. "On quasi-continuous rings" Proc. Amer. Math. Soc. 120.4, John Wiley & Sons Inc. (1994): 1049-1051 | |||
| 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 | |||
| Nicholson, W. Keith. "A short proof of the {W}edderburn-{A}rtin theorem" New Zealand Journal of Mathematics 22.1, John Wiley & Sons Inc. (1993): 83-86 | |||
| Nicholson, W. Keith. "On {PP}-endomorphism rings" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 36.2, John Wiley & Sons Inc. (1993): 227-230 | |||
| 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 | |||
| 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 | |||
| Nicholson, W. Keith. "On {F}aith's correspondence theorem" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 21.1, John Wiley & Sons Inc. (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. "Morita context functors" Mathematical Proceedings of the Cambridge Philosophical Society 103.3, John Wiley & Sons Inc. (1988): 399-408 | |||
| 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. "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 | |||
| 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 and Watters, J. F. "Normal classes of rings and tensor products" Communications in Algebra 9.3 (1981): 299-311 | |||
| 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 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 and Watters, J. F. "The strongly prime radical" Proc. Amer. Math. Soc. 76.2 (1979): 235-240 | |||
| 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. "Local rings with elementary {A}belian units" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 19.2 (1976): 205-208 | |||
| 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. "Commutativity of rings with abelian or solvable units" Proc. Amer. Math. Soc. 56 (1976): 59-62 | |||
| Nicholson, W. Keith. "On semiperfect modules" Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 18.1 (1975): 77-80 | |||
| Nicholson, W. Keith. "{$I$}-rings" Transactions of the American Mathematical Society 207 (1975): 361-373 | |||
| 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 | |||