Increasing Positive Monoids of Ordered Fields Are FF-monoids
TLDR
In this article, it was shown that every increasing positive monoid of an ordered field is an FF-monoid, provided that P ∖ { 0 } does not have 0 as a limit point.About:
This article is published in Journal of Algebra.The article was published on 2019-01-15 and is currently open access. It has received 59 citations till now. The article focuses on the topics: Monoid & Syntactic monoid.read more
Citations
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On the atomicity of monoid algebras
TL;DR: A negative answer to the question of whether a monoid algebra over a field F is atomic provided that both M and R are atomic dates back to the 1980s and was shown in this paper.
Journal ArticleDOI
Factorization invariants of Puiseux monoids generated by geometric sequences
TL;DR: In this paper, the authors study some of the factorization invariants of the class of Puiseux monoids generated by geometric sequences and compare and contrast them with the known results for numerical monoids generat...
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Puiseux monoids and transfer homomorphisms
TL;DR: In this paper, it was shown that transfer homomorphisms from a non-finitely generated atomic Puiseux monoid to a finitely generated monoid do not exist.
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Factorization invariants of Puiseux monoids generated by geometric sequences
TL;DR: In this article, the authors study some of the factorization invariants of Puiseux monoids generated by geometric sequences, and compare and contrast them with the known results for numerical monoid generated by arithmetic sequences.
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On strongly primary monoids, with a focus on Puiseux monoids
TL;DR: In this paper, the authors studied the tameness of strongly primary Puiseux monoids and established an algebraic characterization of globally tame tameness, and obtained a result on the structure of sets of lengths of locally tame strongly primary monoids.
References
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Book
Graduate Texts in Mathematics
Rajendra Bhatia,Glen Bredon,Wolfgang Walter,Joseph J. Rotman,M. Ram Murty,Jane Gilman,Peter Walters,Martin Golubitsky,Ioannis Karatzas,Henri Cohen,Raoul Bott,Gaisi Takeuti,Béla Bollobás,John M. Lee,Jiří Matoušek,Saunders Mac Lane,John L. Kelley,B. A. Dubrovin,Tom M. Apostol,John Stillwell,William Arveson +20 more
Reference BookDOI
Non-Unique Factorizations : Algebraic, Combinatorial and Analytic Theory
TL;DR: In this article, an abstract structure theorem for Sets of Lengths of Powers of an Element has been proposed for finite Abelian groups, which is based on the Dirichlet series.
Book
Finitely Generated Commutative Monoids
TL;DR: A self-contained book on finitely generated commutative monoids with the theory and algorithms needed for the study of the main classical problems related to this kind of monoid is presented in this article.
Journal Article
Sets of lengths do not characterize numerical monoids.
TL;DR: In this article, the sets of length and unions of sets of lengths of numerical monoids are studied and necessary and sufficient conditions for two such monoids to have identical sequences of length sets are given.