Non-Unique Factorizations

By P. A. García-Sánchez. 2010

303 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/960a0c848f643f41e37eb213180e583c71fac1e1

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In Algebra and Number Theory

In Computational Theory and Mathematics

Citations in the corpus

The Interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics (2015, methodology): “In order to distinguish between the group operation in G and the operation in F (G0), we use the symbol · for the multiplication in F (G0), hence F (G0) = ( F (G0), · ) —this coincides with the convention in the monographs [39, 49]–and we denote multiplication in G by juxtaposition of elements.”
Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids (2010, methodology): “The theory of Krull monoids is presented in the monographs [31, 30, 25].”
On the arithmetic of tame monoids with applications to Krull monoids and Mori domains (2010, methodology): “If every class contains a prime divisor, then the main invariants of factorization theory are infinite, and in particular, every finite nonempty set L ⊂ N occurs as a set of lengths (see [32,22] and [24, Theorem 4.”
The large Davenport constant I: Groups with a cyclic, index 2 subgroup (2012, background): “Since that time (dating back to the early 1960s), it has developed into a flourishing branch of Additive and Combinatorial Number Theory (see the surveys [3, 5, 8] or the monographs [12, 10]).”
Inverse zero-sum problems II (2008, methodology): “We refer to the recent survey article [10], the lecture notes [14], the monographs [13], in particular Chapters 5 to 7, and [20], in particular Chapter 9, for detailed information on and applications of Davenport’s constant, e.”
Local tameness of v-noetherian monoids (2008, methodology): “For general information on local tameness and its relevance in factorization theory we refer to [15].”
On the delta set and the Betti elements of a BF-monoid (2012, background): “We note that the reduced assumption is not necessary, since one can always remove the units of S and consider Sred instead of S (see [14] for details).”
Arithmetic of seminormal weakly Krull monoids and domains (2015, background): “2) have found some attention in recent literature ([42, 65, 48]), we want to outline the connection with the present concepts.”
Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules (2016, methodology): “The theory of Krull monoids is presented in the monographs [32, 23].”