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SKEW LATTICES
SKEW LATTICES
Ladies and gentleman, welcome to the amazing world of the skew lattices
During the last years, several authors were interested on the study of specific properties of the skew lattices that relate to fundamental properties of lattices. Unlike what happens in lattices in general, in skew lattices the properties of distributivity and cancellation are independent. In fact, cancellation is related with the property of symmetry that indicates the instances of commutativity in a skew lattice.
A skew lattice is a set S equipped with two associative, idempotent binary operations v and ^ that satisfy the absorption laws (b ^ a)v a = a = a v (a ^ b) and their duals. The class of skew lattices forms a variety largely studied in the past twenty years motivated by semigroup theory and lattice theory. The following authors had a relevant role on its study.
A. Bauer, R. J. Bignall, W. H. Cornish, K. Cvetko-Vah, P. Jordan, M. Kinyon, G. Kudryavtseva,
G. Laslo, J. Leech, J. Pita Costa, H. Radjavi, V. Slav´ık, M. Spinks, R. Veroff
Several are the tools to work with these algebras, some of them comprehending computer reasoning. Prover9 is an automated theorem prover for first-order and equational logic, and Mace4 searches for finite models and counterexamples. Click to get a LIST OF AXIOMS ready to use in Prover 9/Mace 4.
Publications
Publications
M. Kinyon, J. Leech and J. Pita Costa. Distributivity in skew lattices. Semigroup Forum 91 (2015):378-400.
J. Pita Costa and K. Cvetko-Vah. Flat coset decompositions of skew lattices. Semigroup Forum 92 (2016): 361-376.
2014 On the Coset Category of a Skew Lattice. Demonstratio Mathematica. Vol. XLVII No. 3 [in print]
2013 Distributive Skew Lattices. Semigroup Forum. (with J. Leech and M. Kinyon) [submitted]
2012 On the Coset Laws for Distributive Skew Lattices. Portugaliae Mathematica. [submitted]
2012 On the Coset Structure of Skew Lattices. Ph. D. Dissertation (mentored by Karin Cvetko-Vah), University of Ljubljana. [beamer presentation]
2012 On Ideals of a Skew Lattice. Discussiones Mathematicae 32 (2012), 5--21. DOI: doi:10.7151/dmgaa.1187.
2012 Coset Laws for Categorical Skew Lattices. Algebra Universalis. DOI: 10.1007/s00012-012-0194-z.
2011 On the Coset Structure of a Skew Lattice. Demonstratio Mathematica Vol. XLIV No. 4, Conference Proceedings of AAA80.
2011 On the Coset Laws for Skew Lattices. Semigroup Forum Vol. 8 No. 3 (with Karin Cvetko-Vah).
2010 Coset Laws for Skew Lattices in Rings. Novi Sad Journal of Mathematics Vol. 40 No. 3, Conference Proceedings of NSAC 2009 (with Karin Cvetko-Vah). [erratum]
2010 Review article for Wikipedia. Wikipedia (with Jonathan Leech and Karin Cvetko-Vah).
Conference Talks
Conference Talks
2012.06.19 Coset Laws for Skew Lattices. 5th Croatian Mathematical Congress. Rijeka, HR.
2011.07.26 On skew ideals. Groups and Semigroups: Interactions and Computations. Lisbon, PT.
2011.06.24 On ideals for skew lattices. 82th Arbeitstagung Allgemeine Algebra, Potsdam, DE.
2010.05.31 On the coset structure of skew lattices in rings. 6th Linear Algebra Workshop, Kranjska Gora, SI.
2010.06.23 The coset structure of categorical skew lattices, International Conference on Algebras and Lattices, Prague, CZ.
2010.05.30 On the coset structure of categorical skew lattices. 80th Arbeitstagung Allgemeine Algebra, Bedlewo, PL.
2009.09.07 On skew lattices. Summer School on General Algebra and Ordered Sets, Stara Lesna, SK.
2009.08.17 On parallelogram laws for skew lattices. Novi Sad Algebra Conference, Novi Sad, SE. [slides]
2009.08.17 On parallelogram laws for skew lattices. Novi Sad Algebra Conference, Novi Sad, SE. [slides]
Seminar Talks & Workshops
Seminar Talks & Workshops
2012.10.24 Flat coset decomposition of skew lattices. Seminar za Algebro, Fakulteta za Matematika, Ljubljana, SI.
2012.10.23 Contributions to skew lattice theory. Inštitut Jozef Štefan, Ljubljana, SI. [VIDEOLECTURE]
2012.10.04-12 Working seminars on noncommutative lattices. CAUL, University of Lisboa, PT.
2012.03.14 Coset laws for distributivity. Seminar za Algebro, Fakulteta za Matematika, Ljubljana, SI.
2012.02.03 Coset structure decomposition. Seminário de Reticulados, Álgebra Universal e Lógica Algébrica, CAUL, Lisboa, PT.
2011.10.28 Coset structure decomposition. Seminar za Algebro, Fakulteta za Matematika, Ljubljana, SI.
2011.04.11 A categorical approach to skew lattices. Seminar za osnove matematike in teoretične računalništva, FMF, Ljubljana, SI.
2011.02.21 On skew ideals. Seminar za Algebro, Fakulteta za Matematika, Ljubljana, SI.
2010.12.20 On the coset structure of skew lattices. Seminário de Álgebra, CAUL, University of Lisbon, PT.
2010.10.14 On the coset structure of skew lattices. Seminar za Algebro, Fakulteta za Matematika, Ljubljana, SI.
2010.05.03 On categorical skew lattices. Seminar za Algebro, Fakulteta za Matematika, Ljubljana, SI.
2010.01.08 Skew Boolean algebras. CAUL, University of Lisboa, PT.
2009.12.17 On Skew Lattices. CAUL, University of Lisboa, PT.
2009.12.10 Skew Boolean logic. Logic Seminar, MIMS, University of Manchester, UK.
2009.11.24 On parallelogram laws for skew lattices in rings. Seminar za Algebro, Fakulteta za Matematika, Ljubljana, SI.
2009.04.16 On parallelogram laws for skew lattices. Seminar za Algebro, Fakulteta za Matematika, Ljubljana, SI.
2008.09.25 A categorical perspective on skew lattices. Seminar za Algebro, Fakulteta za Matematika, Ljubljana, SI.
Outreach Activities
Outreach Activities
JOÃO PITA COSTA 2016
JOÃO PITA COSTA 2016
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