CV 2020

Jonathan E. Leech
Emeritus Professor
Department of Mathematics, Westmont College
Santa Barbara, California
e-mail: leech@westmont.edu
Education BA (Mathematics), University of Hawaii, May, 1967
Awarded a Woodrow Wilson Fellowship in 1967, but accepted a
National Science Foundation Fellowship to study at UCLA
Ph.D. (Mathematics), UCLA, September, 1969
Experience
Westmont College, 1985–2015, Professor (final level)
McKenzie University, Sao Paulo, Brazil, Visiting Professor, June-July 1992
Universidad de Granada, Granada, Spain, Visiting Professor, June-July 1988
Missouri Western State University, Associate Professor, 1977-1985
Case Western Reserve University, Visiting Associate Professor, 1982-1983
University of Tennessee, Assistant Professor, 1971-1977
Publications (most recent first)
Noncommutative frames revisited (with K. Cvetko-Vah & J. Hemelaer), arXiv:1911.12355.
My journey into noncommutative lattices and their theory, The Art of Discrete and Applied
Mathematics (ADAM), 2 (2019) #P2.01. Published online 7 August, 2019. In the same
issue of this e-journal:
Regular antilattices (with K. Cvetko-Vah, M. Kinyon and T. Pisanski).
On the coset structure of distributive skew lattices (with J. Pita Costa).
Open problems from NCS2018 (with J. Pita Costa).
Pierre Antoine Grillet at 75, Semigroup Forum, 94 (2017), 189-193.
Varieties of skew Boolean algebras with intersections (with M. Spinks), Journal of the
Australian Mathematical Society, 102 (2017), 290-306.
Free skew Boolean algebras (with G. Kudryavtseva), International Journal of Algebra and
Computation, 26 (2016), 1323-1348.
Distributivity in skew lattices (with M. Kinyon and J. Pita Costa), Semigroup Forum, 91 (2015),
378–400.
Skew lattices and binary operations on functions (with K. Cvetko-Vah and M. Spinks),
Journal of Applied Logic, 11 (2013), 253-265.
Categorical skew lattices (with M. Kinyon), Order, 30 (2013), 763 – 777.
Rings whose idempotents form a multiplicative set (with K. Cvetko-Vah), Communications
in Algebra, 40 (2012), 3288 - 3307.
On maximal idempotent-closed subrings of M n (F) (with K. Cvetko-Vah), International
Journal of Algebra and Computation, 21 (2011), 1097-1110.
Cancellation in skew lattices (with K. Cvetko-Vah, M. Kinyon and M. Spinks), Order, 28
(2011), 9 - 32.
Skew Boolean algebras derived from generalized Boolean algebras (with M. Spinks),
Algebra Universalis, 58 (2008), 287-302.

Associativity of the V-operation on bands in rings (with K. Cvetko-Vah), Semigroup
Forum, 76 (2008), 32-50.
Magic squares, finite planes & simple quasilattices, Ars Combinatoria, 77 (2005), 75-96.
Small Skew Lattices in Rings, Semigroup Forum, 70 (2005), 307-311.
Green’s equivalences on noncommutative lattices (with G. Laslo), Acta Scientiarum
Mathematicarum (Szeged), 68 (2002), 501-533.
Symmetric groupoids, free categories and E*-unitary inverse monoids, Proceedings of the
Royal Society of Edinburgh (Series A), 129 (1999), 959-985.
Dual symmetric inverse monoids and representation theory (with D. FitzGerald), Journal
of the Australian Mathematical Society (Series A), 64 (1998), 345-367.
On the foundations of inverse monoids and inverse algebras, Proceedings of the Edinburgh
Mathematical Society, 41 (1998), 1-21.
Recent developments in the theory of skew lattices, Semigroup Forum, 52 (1996), 7-24.
Skew Boolean algebras and discriminator varieties (with R. J. Bignall), Algebra
Universalis, 33 (1995), 387-398.
Inverse monoids with a natural semilattice ordering, Proceedings of the London
Mathematical Society, 70 (1995), 146-182.
The geometric structure of skew lattices, Transactions of the American Mathematical
Society, 335 (1993), 823-845.
Normal skew lattices, Semigroup Forum, 44 (1992), 1-8.
Skew Boolean algebras, Algebra Universalis, 27 (1990), 497-506.
Skew lattices in rings, Algebra Universalis, 26 (1989), 48-72.
Constructing inverse monoids from small categories, Semigroup Forum, 36 (1987), 89-116.
The D-category of a monoid, Semigroup Forum, 34 (1986), 89-116.
Towards a theory of noncommutative lattices, Semigroup Forum, 34 (1986), 117-120.
Cohomology theory for monoid congruences, Houston J. Mathematics, 11 (1985), 207-223.
Extending groups by monoids, Journal of Algebra, 74 (1982), 1-19.
The D-category of a semigroup, Semigroup Forum, 11(1976), 283-296.
The structure of a band of groups, Memoirs of the American Math. Society, 157 (1975), 67-95.
H-coextensions of monoids, Memoirs of the American Math. Society, 157 (1975), 1-66.
Other publications
Triangles with verticies at roots of unity, American Math. Monthly, 87 (1980), 674.
Filling an open set with squares of specified area, American Math. Monthly, 87 (1980), 755-456.
Some Presentations of Research
Noncommutative Structures 2018: a Workshop in Honor of Jonathan Leech (opening talk),
Portoroz, Slovenia, May 2018. (The publicized workshop title was NCS2018.)
Mathematics Seminar, University of Ljubljana, Ljubljana, Slovenia, June 2014.
Mathematics Seminar, University of Tasmania, Hobart, Tasmania, March 2006.
Linear Algebra Workshop, Lake Bled, Slovenia, May 2005.
Algebra Symposium, Babes-Bolyai University, Cluj-Napoca, Romania, May 2005
Special Session on Lattice Theory and Applications, American Mathematical Society,
National Meeting, San Diego, January 2002.
Ninth International Colloquium on Numerical Analysis and Computer Science, Plovdiv, Bulgaria,
August 2000.

Symposium on Universal Algebra and Multiple-Valued Logic, Winter Meeting of the Canadian
Math. Society, Kingston, Ontario, Dec. 1998.
Workshop on Semigroup Theory in Honor of John W. Howie, Lisbon, Portugal, May 1996.
Conference on Semigroup Theory and its Applications in Memory of Alfred H. Clifford,
Tulane University, New Orleans, Louisiana, March 1994.
Special Session on Algebraic Semigroups, Regional Meeting of the American Mathematical
Society, Springfield, Missouri, March 1994.
International Conference on Lattices, Semigroups and Universal Algebras, U. Lisbon, 1988.
Algebra Colloquium, Departamento de Algebra, Universidad de Granada, June 1988.
Ring Theory Seminar, University of California, Santa Barbara, October 1986.
NIH Conference on Universal Algebra and Lattice Theory, Bethesda, Maryland, August 1986.
And numerous other presentations prior to 1986.
Other Scholarly and Professional Activities
Reviewer for Mathematical Reviews.
Referee of numerous articles for various professional journals.
External reader for four doctoral dissertations.
Participant in:
Templeton-Oxford Seminars on Science and Religion, Oxford University Summers 1999–2001.
Workshop on Mathematics in the Arts and Humanities, Dartmouth, July 1998.
Workshop Conference on Universal Algebra and Category Theory, MSRI, Berkeley, July 1993.
20th International Congress of Mathematicians in Berkeley, August 1986.
17th International Congress of Mathematicians in Vancouver, August 1974.
Some publications of others based, at least in part, on my research (For further such publications,
and in particular more recent ones, see references in the above “Journey” article of 2019 in ADAM. See
also other articles in that issue of ADAM, all of which are based on talks given at NCS2018.)
K. Cvetko-Vah, On skew Heyting algebras, Ars Mathematica Contemporanea, 12 (2017), 37-50.
1
M. Calvo-Cervera & A. M. Cegarra, Computability of the (co)homology of cyclic monoids,
International Journal of Algebra and Computation, 26 (2016), 887–910.
G. Kudryavtseva & M. V. Lawson, Boolean sets, skew Boolean algebras and a non-commutative
Stone duality, Algebra Universalis, 75 (2016), 1–19.
K. Cvetko-Vah & A. Salibra, The connection of skew Boolean algebras and discriminator
varieties to Church algebras, Algebra Universalis, 73 (2015), 369–390.
A. Bauer & K. Cvetko-Vah, Stone duality for skew Boolean algebras with intersections,
Houston Journal of Mathematics, 39 (2013), 73–109.
A. Bauer, K. Cvetko-Vah, M. Gerhke & G. Kudryavtseva, and S. van Gool, A noncommutative
Priestly duality, Topology and Applications, 160 (2013), 1423–1438.
G. Kudryavtseva, A dualizing object approach to noncommutative Stone duality, Journal
Australian Math. Society, 95 (2013), 383-403.
G. Kudryavtseva, A refinement of Stone duality to skew Boolean algebras, Algebra Universalis.
67 (2012), 497–506.
J. Pita Costa, Coset laws for categorical skew lattices, Algebra Universalis, 68 (2012), 75–89.
K. Cvetko-Vah, On strongly symmetric skew lattices, Algebra Universalis, 66 (2011), 99–113.
K. Cvetko-Vah & J. Pita Costa, On coset laws for skew lattices, Semigroup Forum, 83 (2011),
395–411.

J. Pita Costa, On the coset structure of a skew lattice, Demonstratio Mathematica, 44 (2011),
673–692.
2
J. Berendsen, D. N. Jansen, J. Schmaltz, & F. W. Vaandrager, The axiomatization of overriding
and update, Journal of Applied Logic, 8 (2010), 141–150.
M. Spinks & R. Veroff, Axiomatizing the skew Boolean propositional calculus, Journal of
Automated Reasoning, 37 (2006), 3–20.
E. D. Schwab, Möbius categories as reduced standard division categories of combinatorial
inverse monoids, Semigroup Forum, 69 (2004), 30–40.
E. D. Schwab, The Möbius category of some combinatorial inverse semigroups, Semigroup
Forum, 69 (2004), 41–50.
R. Bignall & M. Spinks, Implicative BCS-algebra subreducts of skew Boolean algebras,
Scientiae Mathematicae Japonicae, 58 (2003), 629–638.
Corrigendum, Scientiae Mathematicae Japonicae, 66 (2007), 387–390.
E. Aznar & A. Sevilla, Beck, H and Leech Coextensions, Semigroup Forum, 61 (2000), 385–
404.
3
E. Aznar & A. Sevilla, Equivalences between D-categories of inverse monoids, Semigroup
Forum, 59 (1999), 435–452.
C. Wells, Extension Theories for Monoids, Semigroup Forum, 16 (1978), 13–35.
1
In this paper the authors present an unpublished result of mine (the calculation of the cohomology groups
of a cyclic monoid for the case of relevance to H-coextensions of that monoid), acknowledging my priority.
2
In this paper the authors introduced and studied a variety of algebras that are term equivalent to the variety
of left-handed skew Boolean algebras. In so doing they indirectly proved new results of interest about the
latter.
3
Although appearing in print later, information in this paper was crucial in the development and publication
of my earlier 1987 paper, Constructing inverse monoids from small categories, and its 1998 successor, On
the foundations of inverse monoids and inverse algebras.
Even more recent addenda to Some publications of others … (as of April 30, 2020)
R. Koohnavard & A. B. Saeid, On pseudo residuated skew lattices, Boletín de la Sociedad
Matemática Mexicana 3rd Series, (2020) on line first.
K. Cvetko-Vah and C. Verwimp, Skew lattices and set-theoretic solutions of the Yang-
Baxter equation, Journal of Algebra, 542 (2020). 65 – 92.
K. Cvetko-Vah, Jens Hemelaer & Lieven Le Bruyn, Duality for noncommutative frames,
arXiv: 1911.12625 (2019)
Teaching experience: 46 years of teaching mathematics at the college-university level. Courses
taught include:
The full calculus sequence up through multivariable calculus. Linear algebra.
Modern algebra. (Further) Topics in Modern Algebra. Combinatorics
College geometry. Number Theory. History of Mathematics
Statistics – both the freshman level and the advanced (calculus based) level
Formal languages & automata theory.
Graduate modern algebra sequence. Homological algebra. Ring theory.