Workshop on Rigs and Rings.
Venue
Shinshu University, Matsumoto, Japan.
Room: A401 (Building A of Fuclty of Science).
[Maps (in English)]
[Maps etc (in Japanese)]
Schedule
2018 Jan. 18 (Thur.)
 14:40  15:10

Katthaleeya DAOWSUD
(Kasetsart Univ.)
/
แคทลียา ดาวสุด
(มหาวิทยาลัยเกษตรศาสตร์)

On Commutative Prime Gamma Generalized Boolean Semirings

A $\Gamma$generalized Boolean semiring (or simply $\Gamma$GBsemiring) is a triple $(R, +, \Gamma)$ satisfying $(R, +)$ is an abelian group, and $\Gamma$ is a nonempty finite set of binary operations satisfying the following properties: $a \alpha b \in R$ for all $a, b \in R$ and $\alpha \in \Gamma$,
$a \alpha (b + c)$ = $a \alpha b$ + $a \alpha c$ for all $a, b, c \in R$ and $\alpha \in \Gamma$,
$a \alpha (b \beta c)$ = $(a \alpha b) \beta c$ = $(b \alpha a) \beta c$ for all $a, b, c \in R$ and $\alpha, \beta \in \Gamma$,and $a \alpha (b \beta c)$ = $a \beta (b \alpha c)$ for all $a, b, c \in R$ and $\alpha, \beta \in \Gamma$.
In this talk, we investigate the commutativity of a prime $\Gamma$generalized Boolean semiring with certain conditions.
(This talk was based on the joint work with Utsanee Leerawat.
See also this pdf file of this abstract.)

 15:20  15:35

OHARA, Mariko (Shinshu Univ.)
/
小原 まり子 (信州大学)

Algebraic Ktheory and cycles

I talk about the background
of the algebraic Ktheory of an algebraic variety,
from the Grothendieck group for a scheme to the higher
algebraic Ktheory space introduced by Quillen.
I also mention some
cohomology theory
and maps between them.
 15:45  16:00

YAZAWA, Akiko
(Shinshu Univ.)
/
矢澤 明喜子
(信州大学)

The Lefschetz property of an algebra constructed by a graph.

Let $A=\bigoplus_{i=0}^{c}A_{i}$, $A_{c}\neq \boldsymbol{0}$,
be a graded Artinian algebra.
We say that
$A$ has the strong Lefschetz property
if there exists an element $L\in A_{1}$
such that the multiplication map $\times L^{c2i}:A_{i}\to A_{ci}$
is bijective
for each $i\in\{0,1,\ldots, \lfloor\frac{c}{2}\rfloor\}$.
In this presentation,
we consider
an algebra
constructed by the weighted generating function of spanning trees in a graph.
For $n\leq 5$,
we show the strong Lefschetz property
for the algebra corresponding to the complete graph $K_{n}$.
Organizer
If you have any query for this workshop,
please ask
NUMATA, Yasuhide (Shinshu University, nu at math.shinshuu.ac.jp)
by email.