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pro vyhledávání: '"Chapman, Scott T."'
Let $M$ be a Puiseux monoid, that is, a monoid consisting of nonnegative rationals (under addition). A nonzero element of $M$ is called an atom if its only decomposition as a sum of two elements in $M$ is the trivial decomposition (i.e., one of the s
Externí odkaz:
http://arxiv.org/abs/2312.00240
In this paper, we study various factorization invariants of arithmetical congruence monoids. The invariants we investigate are the catenary degree, a measure of the maximum distance between any two factorizations of the same element, the length densi
Externí odkaz:
http://arxiv.org/abs/2210.01224
Autor:
Chapman, Scott T., Polo, Harold
A subset $S$ of an integral domain $R$ is called a semidomain if the pairs $(S,+)$ and $(S, \cdot)$ are semigroups with identities; additionally, we say that $S$ is additively reduced provided that $S$ contains no additive inverses. Given an additive
Externí odkaz:
http://arxiv.org/abs/2209.13817
Autor:
Chapman, Scott T., Gotti, Marly
An additive submonoid of the nonnegative cone of the real line is called a positive monoid. Positive monoids consisting of rational numbers (also known as Puiseux monoids) have been the subject of several recent papers. Moreover, those generated by a
Externí odkaz:
http://arxiv.org/abs/2108.05561
Let $S$ be a nonnegative semiring of the real line, called here a positive semiring. We study factorizations in both the additive monoid $(S,+)$ and the multiplicative monoid $(S\setminus\{0\}, \cdot)$. In particular, we investigate when, for a posit
Externí odkaz:
http://arxiv.org/abs/2103.13264
An atomic monoid $M$ is called a length-factorial monoid (or an other-half-factorial monoid) if for each non-invertible element $x \in M$ no two distinct factorizations of $x$ have the same length. The notion of length-factoriality was introduced by
Externí odkaz:
http://arxiv.org/abs/2101.05441
For a commutative cancellative monoid $M$, we introduce the notion of the length density of both a nonunit $x\in M$, denoted $\mathrm{LD}(x)$, and the entire monoid $M$, denoted $\mathrm{LD}(M)$. This invariant is related to three widely studied inva
Externí odkaz:
http://arxiv.org/abs/2008.06725
A Puiseux monoid is an additive submonoid of the nonnegative rational numbers. If $M$ is a Puiseux monoid, then the question of whether each non-invertible element of $M$ can be written as a sum of irreducible elements (that is, $M$ is atomic) is sur
Externí odkaz:
http://arxiv.org/abs/1908.09227
Publikováno v:
Communications in Algebra, 2019
We study some of the factorization invariants of the class of Puiseux monoids generated by geometric sequences, and we compare and contrast them with the known results for numerical monoids generated by arithmetic sequences. The class we study consis
Externí odkaz:
http://arxiv.org/abs/1904.00219
Autor:
Chapman, Scott T.
Using factorization properties, we give several characterizations for an algebraic number ring to have class number 2.
Externí odkaz:
http://arxiv.org/abs/1903.04606