Isaac Owusu-Mensah
The Athens Algebra Seminar features Isaac Owusu-Mensah discussing “Algebraic structures on the set of all magmas over a fixed set” on Tuesday, March 6, from 4:35 to 5:35 p.m. in Morton 313.
Owusu-Mensah is a graduate student in Mathematics at Ohio University.
Abstract: In recent years, the word magma has been used to designate a pair of the form (S,∗) where ∗ is a binary operation on the set S. Inspired by that terminology, we use the notation M(S) (the magma of S) to denote the set of all binary operations on the set S (i.e. all magmas with underlying set S.) In [1], distributivity hierarchy graphs of a set are introduced. Given a set S, its hierarchy graph has M(S) as vertices and there is an edge from one operation, ∗, to another one, ◦, if ∗ distributes over ◦. Given ∗∈ M(S), the set out(∗) = {◦∈ M(S)|∗ distributes over ◦} is called the outset of ∗. We define an operation that make M(S) a monoid in such a way that each outset is a submonoid. This endowment gives us a possibility to compare the various elements of M(S) with respect to the monoid structure of their outsets. Various properties of the operation mentioned above are considered, including multiple additive structures on M(S) that have it as the multiplicative part of a nearring. (This is a preliminary report on an ongoing project with Sergio R. Lopez-Permouth and Asiyeh Rafieipour.)
[1] Lopez-Permouth and L. H. Rowen, Distributive hierarchies of binary operations, to appear, Contemporary Mathematics series, American Math Soc.
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