9 papers
An unrestricted notion of the finite factorization property
Jonathan Du, Felix Gotti
A nonzero element of an integral domain (or commutative cancellative monoid) is called atomic if it can be written as a finite product of irreducible elements (also called atoms).…
On three families of dense Puiseux monoids
Scott. T. Chapman, Felix Gotti, Marly Gotti +1
A positive monoid is a submonoid of the nonnegative cone of a linearly ordered abelian group. The positive monoids of rank are called Puiseux monoids, and their atomicity, arit…
On the ascent of almost and quasi-atomicity to monoid semidomains
Victor Gonzalez, Felix Gotti, Ishan Panpaliya
A commutative monoid is atomic if every non-invertible element factors into irreducibles (also called atoms), while an integral (semi)domain is atomic if its multiplicative monoid…
On finitary power monoids of linearly orderable monoids
Jiya Dani, Felix Gotti, Leo Hong +2
A commutative monoid is called a linearly orderable monoid if there exists a total order on that is compatible with the monoid operation. The finitary power monoid of a com…
Arithmetic properties encoded in undermonoids
Felix Gotti, Bangzheng Li
Let be a cancellative and commutative monoid. A submonoid of is called an undermonoid if the Grothendieck groups of and coincide. For a given property $\mathfra…
On primality and atomicity of numerical power monoids
Anay Aggarwal, Felix Gotti, Susie Lu
In the first part of this paper, we establish a variation of a recent result by Bienvenu and Geroldinger on the (almost) non-existence of absolute irreducibles in (restricted) powe…