# Felix Gotti: Atomicity in Monoid Domains

# Atomicity in Monoid Domains

**Felix Gotti, Massachusetts Institute of Technology**

**Abstract:** Given a submonoid $M$ of a torsion-free abelian group and a commutative ring $R$, the \emph{monoid algebra} of~$M$ over~$R$, denoted by $R[M]$, is the commutative ring consisting of all polynomial expressions with coefficients in~$R$ and exponents in $M$, with addition and multiplication defined as for polynomial rings. When $R$ is an integral domain, $R[M]$ is also an integral domain, and we often call it a \emph{monoid domain}. A commutative monoid (resp., an integral domain) is called \emph{atomic} provided that each nonunit (resp., nonzero nonunit) factors into atoms (i.e., irreducibles). In this talk, we will discuss some recent progress on the ascent of atomicity and some related properties from the pair $(M,R)$ to the monoid domain $R[M]$.

Predavanju sledi druženje ob prigrizkih.