43 citations · 241 across the 35 of their papers we have counts for
46 papers
Factorizations in algebraic monogenic semidomains
Jiya Dani, Felix Gotti, Bryan Li +1
We study the additive and multiplicative arithmetic of algebraic monogenic semidomains of the form . We first relate their structure to the conjugates of , characterize whe…
An unrestricted notion of the finite factorization property
Jonathan Du, Felix Gotti
A nonzero element of an integral domain (or an element of a commutative cancellative monoid) is called atomic if it is a unit or can be written as a finite product of irreducible e…
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…
One-dimensional monoid algebras and ascending chains of principal ideals
Alan Bu, Felix Gotti, Bangzheng Li +1
An integral domain is called atomic if every nonzero nonunit of factors into irreducibles, while satisfies the ascending chain condition on principal ideals if every as…
Atomicity in integral domains
Jim Coykendall, Felix Gotti
In algebra, atomicity is the study of divisibility by and factorizations into atoms (also called irreducibles). In one side of the spectrum of atomicity we find the antimatter alge…
On the ascent of atomicity to monoid algebras
Felix Gotti, Henrick Rabinovitz
A commutative cancellative monoid is atomic if every non-invertible element factors into irreducibles (also called atoms), while an integral domain is atomic if its multiplicative…
On the subatomicity of polynomial semidomains
Felix Gotti, Harold Polo
A semidomain is an additive submonoid of an integral domain that is closed under multiplication and contains the identity element. Although atomicity and divisibility in integral d…
Factoriality inside Boolean lattices
Khalid Ajran, Felix Gotti
Given a join semilattice with a minimum , the quarks (also called atoms in order theory) are the elements that cover , and for each $x \in S \setminus \{\hat{…
Hereditary atomicity and ACCP in abelian groups
Felix Gotti
A cancellative and commutative monoid is atomic if every non-invertible element of factors into irreducibles (also called atoms), and is hereditarily atomic if every su…
On the atomic structure of torsion-free monoids
Felix Gotti, Joseph Vulakh
Let be a cancellative and commutative (additive) monoid. The monoid is atomic if every non-invertible element can be written as a sum of irreducible elements, which are als…
On the arithmetic of polynomial semidomains
Felix Gotti, Harold Polo
A subset of an integral domain is called a semidomain provided that the pairs and are semigroups with identities. The study of factorizations in integr…
Integral domains and the IDF property
Felix Gotti, Muhammad Zafrullah
An integral domain is called an irreducible-divisor-finite domain (IDF-domain) if every nonzero element of has finitely many irreducible divisors up to associates. The stud…
GLocal: Global Graph Reasoning and Local Structure Transfer for Person Image Generation
Liyuan Ma, Kejie Huang, Dongxu Wei +1
In this paper, we focus on person image generation, namely, generating person image under various conditions, e.g., corrupted texture or different pose. To address texture occlusio…
Atomic semigroup rings and the ascending chain condition on principal ideals
Felix Gotti, Bangzheng Li
An integral domain is called atomic if every nonzero nonunit element factors into irreducibles. On the other hand, an integral domain is said to satisfy the ascending chain conditi…
Divisibility in rings of integer-valued polynomials
Felix Gotti, Bangzheng Li
In this paper, we address various aspects of divisibility by irreducibles in rings consisting of integer-valued polynomials. An integral domain is called atomic if every nonzero no…
Bi-atomic classes of positive semirings
Nicholas R. Baeth, Scott T. Chapman, Felix Gotti
Let be a nonnegative semiring of the real line, called here a positive semiring. We study factorizations in both the additive monoid and the multiplicative monoid $(S\s…
Length-factoriality in commutative monoids and integral domains
Scott T. Chapman, Jim Coykendall, Felix Gotti +1
An atomic monoid is called a length-factorial monoid (or an other-half-factorial monoid) if for each non-invertible element no two distinct factorizations of have…
Bounded and finite factorization domains
David F. Anderson, Felix Gotti
An integral domain is atomic if every nonzero nonunit factors into irreducibles. Let be an integral domain. We say that is a bounded factorization domain if it is atomic an…
On the additive structure of algebraic valuations of polynomial semirings
Jyrko Correa-Morris, Felix Gotti
In this paper, we study factorizations in the additive monoids of positive algebraic valuations of the semiring of polynomials using a methodolo…
Factorizations in upper triangular matrices over information semialgebras
Nicholas R. Baeth, Felix Gotti
An integral domain (or a commutative cancellative monoid) is atomic if every nonzero nonunit element is the product of irreducibles, and it satisfies the ACCP if every ascending ch…
On strongly primary monoids, with a focus on Puiseux monoids
Alfred Geroldinger, Felix Gotti, Salvatore Tringali
Primary and strongly primary monoids and domains play a central role in the ideal and factorization theory of commutative monoids and domains. It is well-known that primary monoids…