5 papers
Toric rings of -polytopes with small rank
Koji Matsushita
The rank of a -dimensional polytope is defined by , where denotes the number of facets of . In this paper, We focus on the toric rings of -polytopes w…
Conic divisorial ideals of toric rings and applications to Hibi rings and stable set rings
Koji Matsushita
In the present paper, we study conic divisorial ideals of toric rings. We provide an idea to determine them and we give a description of the conic divisorial ideals of Hibi rings a…
Torsionfreeness for divisor class groups of toric rings of integral polytopes
Koji Matsushita
In the present paper, we give some sufficient conditions for to be torsionfree, where denote the divisor class group of…
Levelness versus almost Gorensteinness of edge rings of complete multipartite graphs
Akihiro Higashitani, Koji Matsushita
Levelness and almost Gorensteinness are well-studied properties on graded rings as a generalized notion of Gorensteinness. In the present paper, we study those properties for the e…
Conic divisorial ideals and non-commutative crepant resolutions of edge rings of complete multipartite graphs
Akihiro Higashitani, Koji Matsushita
The first goal of the present paper is to study the class groups of the edge rings of complete multipartite graphs, denoted by , where $1 \leq r_1 \leq \…