본문 바로가기
KERD
논문KCI 등재

A characterization of finite factorization positive monoids

Harold Polo
대한수학회 (The Korean Mathematical Society)|2022.07|대한수학회논문집 (Communications of the KMS)|제37권 제3호|pp. 669-679|DOI 10.4134/CKMS.c210270

2

조회

0

다운로드

1

인용

0

참고문헌

키워드

Well-ordered setco-well-ordered setpositive monoidPuiseux monoidsemiringpositive semiringfinite factorization propertyfactorization theory
주제분류수학

초록

We provide a characterization of the \emph{positive monoids} (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

Abstract

We provide a characterization of the \emph{positive monoids} (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

참고문헌 (20)

  1. D.D. Anderson, "Factorization in integral domains", Journal of Pure and Applied Algebra, 69(1), pp.1~19 (1990), Elsevier BV[DOI]
  2. D. Anderson, "Finite factorization domains", Proceedings of the American Mathematical Society, 124(2), pp.389~396 (1996), American Mathematical Society (AMS)[DOI]
  3. Nicholas R. Baeth, "Bi-atomic classes of positive semirings", Semigroup Forum, 103(1), pp.1~23 (2021), Springer Science and Business Media LLC[DOI]
  4. Maria Bras-Amorós, "Increasingly Enumerable Submonoids of R : Music Theory as a Unifying Theme", The American Mathematical Monthly, 127(1), pp.33~44 (2019), Informa UK Limited[DOI]
  5. P. Cesarz, "Commutative algebra and its applications" (2009), Walter de Gruyter
  6. Scott T. Chapman, "When Is a Puiseux Monoid Atomic?", The American Mathematical Monthly, 128(4), pp.302~321 (2021), Informa UK Limited[DOI]
  7. P. M. Cohn, "Bezout rings and their subrings", Mathematical Proceedings of the Cambridge Philosophical Society, 64(2), pp.251~264 (1968), Cambridge University Press (CUP)[DOI]
  8. J. Correa-Morris, "On the additive structure of algebraic valuations cyclic free semirings", arXiv: https:, arxiv.org, pp.pdf, 2008.13073.pdf
  9. Jim Coykendall, "On the atomicity of monoid algebras", Journal of Algebra, 539, pp.138~151 (2019), Elsevier BV[DOI]
  10. Alfred Geroldinger, "Sets of Lengths", The American Mathematical Monthly, 123(10), pp.960~988 (2016), Informa UK Limited[DOI]
  11. Alfred Geroldinger, "On strongly primary monoids, with a focus on Puiseux monoids", Journal of Algebra, 567, pp.310~345 (2021), Elsevier BV[DOI]
  12. A. Geroldinger, "Non-unique factorizations", pp.2006, Chapman & Hall
  13. R. Gilmer, "Commutative semigroup rings" (1984), University of Chicago Press
  14. Felix Gotti, "Increasing positive monoids of ordered fields are FF-monoids", Journal of Algebra, 518, pp.40~56 (2019), Elsevier BV[DOI]
  15. Felix Gotti, "Atomicity and boundedness of monotone Puiseux monoids", Semigroup Forum, 96(3), pp.536~552 (2017), Springer Science and Business Media LLC[DOI]
  16. Anne Grams, "Atomic rings and the ascending chain condition for principal ideals", Mathematical Proceedings of the Cambridge Philosophical Society, 75(3), pp.321~329 (1974), Cambridge University Press (CUP)[DOI]
  17. Franz Halter-Koch, "Finiteness theorems for factorizations", Semigroup Forum, 44(1), pp.112~117 (1992), Springer Science and Business Media LLC[DOI]
  18. B. H. Neumann, "On ordered division rings", Trans. Amer. Math. Soc, 66, pp.202~252 (1949)[DOI]
  19. Harold Polo, "On the sets of lengths of Puiseux monoids generated by multiple geometric sequences", 대한수학회논문집, 35(4), pp.1057~1073 (2020), 대한수학회[DOI]
  20. J. C. Rosales, "Numerical semigroups" (2009), Springer

관련 논문AI추천

A weaker notion of the finite factorization propertyHenry Jiang, Hwisoo Kim, Shihan Kanungo대한수학회 · 대한수학회논문집2024 · 제39권 제2호On the sets of lengths of Puiseux monoids generated by multiple geometric sequencesHarold Polo대한수학회 · 대한수학회논문집2020 · 제35권 제4호On the internal sum of Puiseux monoidsBryan Li, Jonathan Du, Shaohuan Zhang강원경기수학회 · 한국수학논문집2024 · 제32권 제4호Factorizations into irreducible numerical semigroupsPedro A. Garcıa-Sanchez대한수학회 · 대한수학회논문집2025 · 제40권 제3호A characterization of class groups via sets of lengthsAlfred Geroldinger, Wolfgang Alexander Schmid대한수학회 · 대한수학회지2019 · 제56권 제4호On separative refinement monoidsHuanyin Chen대한수학회 · 대한수학회보2009 · 제46권 제3호

이 간행물의 다른 논문 (22건)

Mean values of derivatives of quadratic prime Dirichlet $L$-functions in function fields정환엽pp. 635-648Semi-neutral groupoids and $BCK$-algebras서영주, 김희식, Joseph Neggerspp. 649-658Commutativity criteria of prime rings involving two endomorphismsSouad Dakir, Abdellah Mamouni, Mohammed Tamekkantepp. 659-667On partial sums of four parametric Wright functionMuhey U. Dinpp. 681-692Infinitely many homoclinic solutions for damped vibration systems with locally defined potentialsMohsen Timoumi, Wafa Selmipp. 693-703
원문 보기