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Joachim "Jim" Lambek (5 December 1922 - 23 June 2014) was Peter Redpath Emeritus Professor of Pure Mathematics at McGill University, where he earned his Ph.D. degree in 1950 with Hans Zassenhaus as advisor.
Lambek supervised 16 doctoral students, and has 51 doctoral descendants. He has over 100 publications listed in the Mathematical Reviews, including 6 books. His earlier work was mostly in module theory, especially torsion theories, non-commutative localization, and injective modules. One of his earliest papers, Lambek & Moser (1954), proved the Lambek-Moser theorem about integer sequences. His more recent work is in pregroups and formal languages; his earliest work in this field were probably Lambek (1958) and Lambek (1979). He is noted, among other things, for the Lambek calculus, an effort to capture mathematical aspects of natural language syntax in logical form and a work that has been very influential in computational linguistics, as well as for developing the connections between typed lambda calculus and cartesian closed categories (see Curry-Howard-Lambek correspondence). His last works were on pregroup grammar.
- Fine, N. J.; Gillman, Leonard; Lambek, Joachim (1966), Rings of quotients of rings of functions, McGill University Press, MR 0200747
- Lambek, Joachim (1966), Lectures on rings and modules, With an appendix by Ian G. Connell, Blaisdell Publishing, MR 0206032; 3rd edition. 2009.
- Lambek, Joachim (1966), Completions of categories, Seminar lectures given in 1966 in Zürich. Lecture Notes in Mathematics, No. 24, Berlin, New York: Springer-Verlag, MR 0209330
- Lambek, Joachim (1971), Torsion theories, additive semantics, and rings of quotients, With an appendix by H. H. Storrer on torsion theories and dominant dimensions. Lecture Notes in Mathematics, Vol. 177, Berlin, New York: Springer-Verlag, MR 0284459
- Lambek, J.; Scott, P.J. (1986), Introduction to Higher Order Categorical Logic, Cambridge University Press, ISBN 978-0-521-35653-4, MR 0856915
- Anglin, W. S.; Lambek, Joachim (1995), The heritage of Thales, Undergraduate Texts in Mathematics, Berlin, New York: Springer-Verlag, ISBN 978-0-387-94544-6, MR 1369087
- Casadio, Claudia; Lambek, Joachim (2008), Computational Algebraic Approaches to Natural Language, Polimetrica, ISBN 978-88-7699-125-7
- Lambek, J. (2008), From word to sentence: a computational algebraic approach to grammar, Polimetrica, ISBN 978-88-7699-117-2
- Lambek, Joachim; Moser, L. (1954), "Inverse and Complementary Sequences of Natural Numbers", The American Mathematical Monthly, The American Mathematical Monthly, Vol. 61, No. 7, 61 (7): 454-458, doi:10.2307/2308078, ISSN 0002-9890, JSTOR 2308078, MR 0062777
- Lambek, J. (1958), "The Mathematics of Sentence Structure", The American Mathematical Monthly, The American Mathematical Monthly, Vol. 65, No. 3, 65 (3): 154-170, doi:10.2307/2310058, ISSN 0002-9890, JSTOR 1480361
- Lambek, Joachim (1972), "Bicommutators of nice injectives", Journal of Algebra, 21: 60-73, doi:10.1016/0021-8693(72)90034-8, ISSN 0021-8693, MR 0301052
- Lambek, Joachim (1972), "Localization and completion", Journal of Pure and Applied Algebra, 2 (4): 343-370, doi:10.1016/0022-4049(72)90011-4, ISSN 0022-4049, MR 0320047
- Lambek, Joachim (1979), "A mathematician looks at Latin conjugation", Theoretical Linguistics, 6 (2): 221-234, doi:10.1515/thli.1979.6.1-3.221, ISSN 0301-4428, MR 0589163
- Casadio, Claudia; Coeke, Bob; Moortgat, Michael; Scott, Philip, eds. (2014), Categories and Types in Logic, Language, and Physics: Essays Dedicated to Jim Lambek on the Occasion of His 90th Birthday, Springer-Verlag