Universal Algebra and Logic

Spring 2008 Seminars

Time: Tuesday, April 22. (SC 1432, 4:10 – 5:30 p.m.)
Speaker: Carmela Sica, University of Salerno
Title: Centralizers in locally finite groups
Abstract: Let G be a locally finite group admitting an automorphism f of finite order such that the centralizer C_G(f) satisfies certain finiteness conditions. What impact does this have on the structure of the group G? Starting from some nown results, it will be shown that if G is locally finite and admits a four-group of automorphisms without non-trivial fixed points, then the derived subgroup G’ is a product of normal nilpotent subgroups. This is joint work with Pavel Shumyatsky.

Time: Tuesday, April 8. (SC 1432, 4:10 – 5:30 p.m.)
Speaker: Matthew Gould, Vanderbilt University
Title: Interassociativity
Abstract: Semigroups (S, #) and (S, *) are said to interassociate with each other if the algebra (S, # , *) satisfies the equations (x#y)*z = x#(y*z) and (x*y)#z = x*(y#z). Old and new results on interassociativity and related topics will be reviewed.

Time: Friday, March 28. (SC 1310, 1:10 – 2:30 p.m.)
Speaker: Petar Markovic, University of Novi Sad, Serbia

Time: Tuesday, March 11. (SC 1432, 4:10 – 5:30 p.m.)
Speaker: Rostislav Horcik, Czech Academy of Sciences
Title: Applications of non-formally-integral totally ordered monoids in non-classical logics
Speaker: Petr Cintula, Czech Academy of Sciences
Title: Hierarchies of implications and disjunctions in non-classical logics

Time: Tuesday, February 26. (SC 1432, 4:10 – 5:30 p.m.)
Speaker: Yuri Bahturin
Title: Functional Identities and Graded Algebras
Abstract: Functional identities are the identical relations for arbitrary functions on algebras. This is a comparatively new piece of techniques which was recently successfully used in the study of Lie, Jordan and other types of maps on associative algebras to prove famous Herstein conjectures. This is summarized in a recent monograph “Functional Identities” by M. Bresar, M. Chebotar and W. Martindale. It was recently discovered that using elementary techniques of Hopf algebras these results can be applied to the study of graded algebras.

Time: Tuesday, February 12. (SC 1432, 4:10 – 5:30 p.m.)
Speaker: Ciro Russo, Vanderbilt University
Title: Propositional deductive systems: hidden interpretability, fragments and equivalence.
Abstract: The interpretability of one logic into another is a very common issue in Mathematical Logic but, as far as we know, a precise and general definition of the concept of “interpretation” is still lacking, the meaning of this word usually relying on a logician’s intuition. We propose a general and purely syntactic definition of interpretability for the case of propositional deductive systems. Then we generalize this definition, together with the notions of equivalence of deductive systems and a fragment of a logic, to corresponding “hidden” notions. Such generalizations are amenable to an algebraic characterization that, under additional hypotheses, yield results for the corresponding non-hidden notions.

Time: Monday, February 4. (SC 1310, 1:10 – 2:30 p.m.)
Speaker: Olga Sapir, Vanderbilt University
Title: Finitely generated permutative varieties (Part II).

Time: Monday, January 28. (SC 1310, 1:10 – 2:30 p.m.)
Speaker: Olga Sapir, Vanderbilt University
Title: Finitely generated permutative varieties (Part I).
Abstract: We show that there exists an algorithm which decides whether a finite set of identities containing a permutation identity defines a variety generated by a finite semigroup or not.

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Vanderbilt University
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Phone: (615) 322-6672
Fax: (615) 343-0215