Workshop on Rigs and Rings.


Shinshu University, Matsumoto, Japan.

Room: A-401 (Building A of Fuclty of Science).

[Maps (in English)] [Maps etc (in Japanese)]


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 $\Gamma$-GB-semiring) 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 K-theory and cycles
I talk about the background of the algebraic K-theory of an algebraic variety, from the Grothendieck group for a scheme to the higher algebraic K-theory 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 $\times L^{c-2i}:A_{i}\to A_{c-i}$ 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 $K_{n}$.


If you have any query for this workshop, please ask NUMATA, Yasuhide (Shinshu University, nu at by e-mail.