Kurzbeschreibung: On the Ascent of Atomicity to Monoid Algebras Abstract Given a submonoid M of a torsion-free abelian group and a commutative ring R, the 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. Observe that if the monoid M is taken to be the additive monoid Z≥0, then R[M ] is the polynomial ring R[x] in an indeterminate x with coefficients in R. Moreover, if F is a field (or a UFD), then the polynomial ring F [x] is atomic, that is, every nonzero polynomial in F [x] factors into irreducible polynomials. More generally, is this also true if we take the exponents of polynomials over F in a more general atomic monoid as, for instance, an additive submonoid of Q≥0? This and further related questions will be answered as part of this talk