Dear Colleagues,

You are most cordially invited to the Yeditepe Mathematics Department 25th Year Seminars organized by the Department of Mathematics. The details of this week's talk are as follows:

**Title:** Socle of Incidence Rings

**Speaker:** Müge Kanuni Er (Düzce Üniversitesi)

**Abstract:** In his seminal paper of 1964, "On the foundations of combinatorial theory I: Theory of Möbius Functions" Gian-Carlo Rota defined an incidence ring as a tool for solving combinatorial problems. Incidence ring is a specific ring of functions defined on the ordered pairs of a given partially ordered set to a given ring. Möbius function is an element of an incidence ring, besides with the appropriate choice of the partially ordered set, Möbius function of this incidence algebra coincides with the well-known Möbius function of number theory. A product of copies of a ring and upper triangular matrices are typical examples of incidence algebras.

The investigation of a ring is usually enriched by understanding special types of ideals of it, such as the Jacobson radical, the prime radical, the socle,the singular ideal, the center, etc. Although incidence rings have been an object of study for a few decades, there does not seem to be any results in the literature on the socle of incidence rings.

In this talk, we will be restricting the left socle of an incidence ring between two sets.More explicitly, we compute the socle of an incidence ring I(X,R) under some assumptions on the ring R and/or the partially ordered set X. (This joint work with Özkay Özkan: doi.org/10.15672/hujms.684042 )

**Date:** Friday, April 16, 2021

**Time:** 13:00

**Place:** Contact Asst. Prof. Dr. Mehmet Akif ERDAL (mehmet.erdal@yeditepe.edu.tr).

You can find a copy of the flyer in this link. *For a full list of this semester's seminar schedule, click on the link below!*

https://researchseminars.org/seminar/7tepemathseminars

Zoom: Contact Asst. Prof. Dr. Mehmet Akif ERDAL (mehmet.erdal@yeditepe.edu.tr) for the address.