24-10-2024
The Center of Mathematics and Applications (NOVA Math), promote the Seminar of Algebra and Logic with the title: “When a Ring meets a Lattice”. João Dias (CIMA, Universidade de Évora) is the speaker.
Abstract: The rational numbers have been used to measure quantities since ancient times; however, their implementation in computer languages raises a significant problem: zero has no inverse. To address this issue, J. Bergstra and J. Tucker introduced an algebraic structure called a meadow, which allows for the inversion of zero.
In this talk, I will introduce meadows and their various classes, demonstrating that they correspond to labelled lattices, where the rings label the vertices. We will explore how concepts from ring theory, such as Artinian rings and decomposition theorems, can be adapted to this new context. Finally, I will present a connection between meadows and sheaves over a topological space, highlighting the implications of this relationship.
Monday, 28 October 2024, at 14:00.