A characterization of arithmetical invariants by the monoid of relations

A characterization of arithmetical invariants by the monoid of relations II: The monotone catenary degree and applications to semigroup rings

The investigation and classification of non-unique factorization phenomena has attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P.A. García-Sánchez, together with several co-authors, derived a method to calculate the catenary and tame degree from the monoid of relations. Then, in [1], the algebraic structure of this approach was investigated and the restriction to finitely generated monoids was removed. We now extend these ideas further to the monotone catenary degree and then apply all these results to the explicit computation of arithmetical inva…

Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids

Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.

算术同余幺半群中不可约元素的周期性

On the periodicity of irreducible elements in arithmetical congruence monoids

本文研究算术同余幺半群 M_{a,b} 中不可约元素的渐近规律，并给出其序列最终具有周期性时关于参数 a、b 的刻画。

A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions

Let H be a Krull monoid with finite class group G and suppose that every class contains a prime divisor. Then sets of lengths in H have a well-defined structure which just depends on the class group G. With methods from additive combinatorics we establish a characterization of those class groups G guaranteeing that all sets of lengths are (almost) arithmetical progressions.

算术同余幺半群的原子密度

Atomic density of arithmetical congruence monoids

本文刻画了算术同余幺半群 $M_{a,b}$ 中原子（不可分解为非单位乘积的元素）的极限比例，即原子密度，并用参数 $a$ 和 $b$ 给出了其完整刻画。

Factorization Properties of Leamer Monoids

The Huneke-Wiegand conjecture has prompted much recent research in Commutative Algebra. In studying this conjecture for certain classes of rings, García-Sánchez and Leamer construct a monoid S_Γ^s whose elements correspond to arithmetic sequences in a numerical monoid Γof step size s. These monoids, which we call Leamer monoids, possess a very interesting factorization theory that is significantly different from the numerical monoids from which they are derived. In this paper, we offer much of the foundational theory of Leamer monoids, including an analysis of their atomic structure, and inves…