[Turkmath:4857] Seminar on April 16, 2021 at 13:00 via Zoom

[Mehmet Akif Erdal]

Dear list members,

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 (please note the unusual time):

Title: Socle of Incidence Rings

Speaker: Müge Kanuni Er (Düzce University)

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
Zoom: Please contact me for the link.

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