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pro vyhledávání: '"Gotti, Felix"'
An integral domain $R$ is called atomic if every nonzero nonunit of $R$ factors into irreducibles, while $R$ satisfies the ascending chain condition on principal ideals if every ascending chain of principal ideals of $R$ stabilizes. It is well known
Externí odkaz:
http://arxiv.org/abs/2409.00580
Autor:
Coykendall, Jim, Gotti, Felix
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 algebraic structures, inside which there are no atoms and, therefore, divi
Externí odkaz:
http://arxiv.org/abs/2406.02503
Autor:
Geroldinger, Alfred, Gotti, Felix
We construct monoid algebras which satisfy the ascending chain condition on principal ideals and which have the property that every nonempty subset of $\mathbb{N}_{\ge 2}$ occurs as a length set.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/2404.11494
Autor:
Gotti, Felix, Krause, Ulrich
The primary purpose of this paper is to generalize the classical Riemann zeta function to the setting of Krull monoids with torsion class groups. We provide a first study of the same generalization by extending Euler's classical product formula to th
Externí odkaz:
http://arxiv.org/abs/2401.06353
Autor:
Gotti, Felix, Rabinovitz, Henrick
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 monoid is atomic. Back in the eighties, Gilmer posed the question of w
Externí odkaz:
http://arxiv.org/abs/2310.18712
Autor:
Gotti, Felix, Polo, Harold
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 domains have been systematically investigated for more than thirty year
Externí odkaz:
http://arxiv.org/abs/2306.01373
Autor:
Ajran, Khalid, Gotti, Felix
Given a join semilattice $S$ with a minimum $\hat{0}$, the quarks (also called atoms in order theory) are the elements that cover $\hat{0}$, and for each $x \in S \setminus \{\hat{0}\}$ a factorization (into quarks) of $x$ is a minimal set of quarks
Externí odkaz:
http://arxiv.org/abs/2305.00413
Autor:
Gotti, Felix
A cancellative and commutative monoid $M$ is atomic if every non-invertible element of $M$ factors into irreducibles (also called atoms), and $M$ is hereditarily atomic if every submonoid of $M$ is atomic. In addition, $M$ is hereditary ACCP if every
Externí odkaz:
http://arxiv.org/abs/2303.01039
Autor:
Gotti, Felix, Vulakh, Joseph
Publikováno v:
Semigroup Forum, 107:402-423 (2023)
Let $M$ be a cancellative and commutative (additive) monoid. The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements, which are also called atoms. Also, $M$ satisfies the ascending chain condition on p
Externí odkaz:
http://arxiv.org/abs/2212.08347
Autor:
Gotti, Felix, Li, Bangzheng
An integral domain $R$ is atomic if each nonzero nonunit of $R$ factors into irreducibles. In addition, an integral domain $R$ satisfies the ascending chain condition on principal ideals (ACCP) if every increasing sequence of principal ideals (under
Externí odkaz:
http://arxiv.org/abs/2212.06213