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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2020.1
- 수록면
- 1,057 - 1,073 (17page)
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In this paper, we study some of the factorization aspects of rational multicyclic monoids, that is, additive submonoids of the nonnegative rational numbers generated by multiple geometric sequences. In particular, we provide a complete description of the rational multicyclic monoids $M$ that are hereditarily atomic (i.e., every submonoid of $M$ is atomic). Additionally, we show that the sets of lengths of certain rational multicyclic monoids are finite unions of multidimensional arithmetic progressions, while their unions satisfy the Structure Theorem for Unions of Sets of Lengths. Finally, we realize arithmetic progressions as the sets of distances of some additive submonoids of the nonnegative rational numbers.
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참고문헌 (32)
참고문헌 신청
D. Bachman / 2014 / Factorizations of upper triangular matrices / Linear Algebra Appl 450:138~157
N. R. Baeth / 2014 / Monoids of modules and arithmetic of direct-sum decompositions / Pacific J. Math 271(2):257~319
C. Bowles / 2006 / On delta sets of numerical monoids / J. Algebra Appl 5(5):695~718
S. T. Chapman / 2010 / Delta sets of numerical monoids using nonminimal sets of generators / Comm. Algebra 38(7):2622~2634
S. T. Chapman / 2020 / Factorization invariants of Puiseux monoids generated by geometric sequences / Comm. Algebra 48(1):380~396
N. R. Baeth / 2014 / Monoids of modules and arithmetic of direct-sum decompositions / Pacific J. Math 271(2):257~319
C. Bowles / 2006 / On delta sets of numerical monoids / J. Algebra Appl 5(5):695~718
S. T. Chapman / 2010 / Delta sets of numerical monoids using nonminimal sets of generators / Comm. Algebra 38(7):2622~2634
S. T. Chapman / 2020 / Factorization invariants of Puiseux monoids generated by geometric sequences / Comm. Algebra 48(1):380~396
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