References
- Anderson, D. D., Anderson, D. F., Zafrullah, M. (1990). Factorization in integral domains. J. Pure Appl. Algebra 69(1):1–19. DOI: https://doi.org/10.1016/0022-4049(90)90074-R.
- Baeth, N. R., Gotti, F. Factorizations in upper triangular matrices over information semialgebras. J. Algebra (to appear). [arXiv:2002.09828].
- Campanini, F., Facchini, A. (2019). Factorizations of polynomials with integral non-negative coefficients. Semigroup Forum. 99(2):317–332. DOI: https://doi.org/10.1007/s00233-018-9979-5.
- Cesarz, P., Chapman, S. T., McAdam, S., Schaeffer, G. J. (2009). Elastic properties of some semirings defined by positive systems. In: Fontana, M., Kabbaj, S. E., Olberding, B., Swanson, I., eds. Commutative Algebra and Its Applications – Proceedings of the Fifth International Fez Conference on Commutative Algebra and Its Applications. Berlin: Walter de Gruyter, pp. 89–101.
- Chapman, S. T., Gotti, F., Gotti, M. (2020). Factorization invariants of Puiseux monoids generated by geometric sequences. Commun. Algebra 48(1):380–396. DOI: https://doi.org/10.1080/00927872.2019.1646269.
- Chapman, S. T., Gotti, F., Gotti, M. When is a Puiseux monoid atomic? Amer. Math. Monthly. (to appear). [arXiv:1908.09227v2].
- Coykendall, J., Gotti, F. (2019). On the atomicity of monoid algebras. J. Algebra 539:138–151. DOI: https://doi.org/10.1016/j.jalgebra.2019.07.033.
- García-Sánchez, P. A., Rosales, J. C. (2009). Numerical Semigroups, Developments in Mathematics, Vol. 20. New York: Springer-Verlag.
- Geroldinger, A. (2016). Sets of lengths. Amer. Math. Monthly. 123:960–988.
- Geroldinger, A., Halter-Koch, F. (2006). Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory, Pure and Applied Mathematics, Vol. 278. Boca Raton, FL: Chapman & Hall/CRC.
- Gilmer, R. (1984). Commutative Semigroup Rings. Chicago Lectures in Mathematics. London: The University of Chicago Press.
- Golan, J. S. (1999). Semirings and Their Applications. Dordrecht, Netherlands: Kluwer Academic Publishers.
- Gotti, F. (2017). On the atomic structure of Puiseux monoids. J. Algebra Appl. 16(7):1750126. DOI: https://doi.org/10.1142/S0219498817501262.
- Gotti, F. (2018). Puiseux monoids and transfer homomorphisms. J. Algebra 516:95–114. DOI: https://doi.org/10.1016/j.jalgebra.2018.08.026.
- Gotti, F. (2019). Increasing positive monoids of ordered fields are FF-monoids. J. Algebra 518:40–56. DOI: https://doi.org/10.1016/j.jalgebra.2018.10.010.
- Gotti, F., Gotti, M. (2018). Atomicity and boundedness of monotone Puiseux monoids. Semigroup Forum. 96(3):536–552. DOI: https://doi.org/10.1007/s00233-017-9899-9.
- Grams, A. (1974). Atomic rings and the ascending chain condition for principal ideals. Math. Proc. Camb. Phil. Soc. 75(3):321–329. DOI: https://doi.org/10.1017/S0305004100048532.
- Polo, H. On the sets of lengths of Puiseux monoids generated by multiple geometric sequences. Commun. Korean Math. Soc. (to appear). [arXiv:2001.06158].
- Ponomarenko, V. (2015). Arithmetic of semigroup semirings. Ukr. Math. J. 67(2):243–266. DOI: https://doi.org/10.1007/s11253-015-1077-1.
- Roitman, M. (1993). Polynomial extensions of atomic domains. J. Pure Appl. Algebra 87(2):187–199. DOI: https://doi.org/10.1016/0022-4049(93)90122-A.
- Rudin, W. (1976). Principles of Mathematical Analysis, 3rd ed. New York: McGraw-Hill.
- Zaks, A. (1982). Atomic rings without a.c.c on principal ideals. J. Algebra 74(1):223–231. DOI: https://doi.org/10.1016/0021-8693(82)90015-1.