Factorization invariants of Puiseux monoids generated by geometric sequences

References

• Amos, J., Chapman, S. T., Hine, N., Paixao, J. (2007). Sets of lengths do not characterize numerical monoids. Integers 7:A50.
   Google Scholar
• Anderson, D. F., Chapman, S. T., Kaplan, N., Torkornoo, D. (2011). An algorithm to compute ω-primality in a numerical monoid. Semigroup Forum 82(1):96–108. DOI:10.1007/s00233-010-9259-5.
   Web of Science ®Google Scholar
• Assi, A., García-Sánchez, P. A. (2016). Numerical Semigroups and Applications. New York: RSME Springer Series, Springer.
   Google Scholar
• Baeth, N., Smertnig, D. (2018). Arithmetical invariants of local quaternion orders. Acta Arith. 186(2):143–177. DOI:10.4064/aa170601-13-8.
   Web of Science ®Google Scholar
• Barron, T., O’Neill, C., Pelayo, R. (2016). On dynamic algorithms for factorization invariants in numerical monoids. Math. Comp. 86(307):2429–2447. DOI:10.1090/mcom/3160.
   Web of Science ®Google Scholar
• Bowles, C., Chapman, S., Kaplan, N., Reiser, D. (2006). On Delta sets of numerical monoids. J. Algebra Appl. 5(5):695–718. DOI:10.1142/S0219498806001958.
   Web of Science ®Google Scholar
• Blanco, V., García-Sánchez, P. A., Geroldinger, A. (2011). Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and krull monoids. Illinois J. Math. 55(4):1385–1414. DOI:10.1215/ijm/1373636689.
   Google Scholar
• Chapman, S. T., Corrales, M., Miller, A., Miller, C., Patel, D. (2017). The catenary degrees of elements in numerical monoids generated by arithmetic sequences. Comm. Algebra 45(12):5443–5452. DOI:10.1080/00927872.2017.1310878.
   Web of Science ®Google Scholar
• Chapman, S. T., Daigle, J., Hoyer, R., Kaplan, N. (2010). Delta sets of numerical monoids using nonminimal sets of generators. Comm. Algebra 38(7):2622–2634. DOI:10.1080/00927870903045165.
   Web of Science ®Google Scholar
• Chapman, S. T., García-Sánchez, P. A., Llena, D. (2009). The catenary and tame degree of numerical monoids. Forum Math. 21:117–129.
   Web of Science ®Google Scholar
• Chapman, S., Holden, M., Moore, T. (2006). Full elasticity in atomic monoids and integral domains. Rocky Mt. J. Math. 36(5):1437–1455. DOI:10.1216/rmjm/1181069375.
   Web of Science ®Google Scholar
• Chapman, S. T., Hoyer, R., Kaplan, N. (2009). Delta sets of numerical monoids are eventually periodic. Aequ. Math. 77(3):273–279. DOI:10.1007/s00010-008-2948-4.
   Web of Science ®Google Scholar
• Chapman, S. T., Kaplan, N., Lemburg, T., Niles, A., Zlogar, C. (2014). Shifts of generators and Delta sets of numerical monoids. Int. J. Algebra Comput. 24(5):655–669. DOI:10.1142/S0218196714500271.
   Web of Science ®Google Scholar
• Colton, S., Kaplan, N. (2017). The realization problem for Delta sets of numerical semigroups. J. Commut. Algebra. 9(3):313–339. DOI:10.1216/JCA-2017-9-3-313.
   Web of Science ®Google Scholar
• Fan, Y., Geroldinger, A., Kainrath, F., Tringali, S. (2017). Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules. J. Algebra Appl. 11:1750234. DOI:10.1142/S0219498817502346.
   Web of Science ®Google Scholar
• García-García, J., Moreno-Frías, M., Vigneron-Tenorio, A. (2015). Computation of the ω-primality and asymptotic ω-primality with applications to numerical semigroups. Isr. J. Math. 206(1):395–411. DOI:10.1007/s11856-014-1144-6.
   Web of Science ®Google Scholar
• García-Sánchez, P., O’Neill, C., Webb, G. (2019). On the computation of factorization invariants for affine semigroups. J. Algebra Appl. 18(1):1950019. DOI:10.1142/S0219498819500191.
   Web of Science ®Google Scholar
• García-Sánchez, P. A., Rosales, J. C. (2009). Numerical Semigroups, Developments in Mathematics, Vol. 20. New York: Springer-Verlag.
   Google Scholar
• Geroldinger, A. (2016). Sets of lengths. Amer. Math. Monthly. 123:960–988.
   Web of Science ®Google Scholar
• Geroldinger, A., Halter-Koch, F. (2006). Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory, Pure and Applied Mathematics, Vol. 278. Boca Raton: Chapman & Hall/CRC.
   Google Scholar
• Geroldinger, A., Hassler, W. (2008). Local tameness of v-noetherian monoids. J. Pure Appl. Algebra 212(6):1509–1524. DOI:10.1016/j.jpaa.2007.10.020.
   Web of Science ®Google Scholar
• Geroldinger, A., Kainrath, F. (2010). On the arithmetic of tame monoids with applications to Krull monoids and Mori domains. J. Pure Appl. Algebra 214(12):2199–2218. DOI:10.1016/j.jpaa.2010.02.023.
   Web of Science ®Google Scholar
• Geroldinger, A., Schmid, W. (2018). A realization theorem for sets of lengths in numerical monoids. Forum Math. 30(5):1111–1118. DOI:10.1515/forum-2017-0180.
   Web of Science ®Google Scholar
• Geroldinger, A., Schmid, W. A., Zhong, Q. (2017). Systems of sets of lengths: Transfer Krull monoids versus weakly Krull monoids. In: M. Fontana, S. Frisch, S. Glaz, F. Tartarone, P. Zanardo, eds. Rings, Polynomials, and Modules. Cham: Springer.
   Google Scholar
• Geroldinger, A., Zhong, Q. (2019). Sets of arithmetical invariants in transfer krull monoids. J. Pure Appl. Algebra 223(9):3889–3918. DOI:10.1016/j.jpaa.2018.12.011.
   Web of Science ®Google Scholar
• Gotti, F. (2019). Increasing positive monoids of ordered fields are FF-monoids. J. Algebra 518:40–56. DOI:10.1016/j.jalgebra.2018.10.010.
   Web of Science ®Google Scholar
• Gotti, F. (2017). On the atomic structure of Puiseux monoids. J. Algebra Appl. 16(7):1750126. DOI:10.1142/S0219498817501262.
   Web of Science ®Google Scholar
• Gotti, F. On the system of sets of lengths and the elasticity of submonoids of a finite-rank free commutative monoid. J. Algebra Appl. (to appear). [arXiv:1806.11273] DOI:10.1142/S0219498820501376.
   Web of Science ®Google Scholar
• Gotti, F. (2018). Puiseux monoids and transfer homomorphisms. J. Algebra 516:95–114. DOI:10.1016/j.jalgebra.2018.08.026.
   Web of Science ®Google Scholar
• Gotti, F. (2019). Systems of sets of lengths of Puiseux monoids. J. Pure Appl. Algebra 223(5):1856–1868. DOI:10.1016/j.jpaa.2018.08.004.
   Web of Science ®Google Scholar
• Gotti, F., Gotti, M. (2018). Atomicity and boundedness of monotone Puiseux monoids. Semigroup Forum 96(3):536–552. DOI:10.1007/s00233-017-9899-9.
   Web of Science ®Google Scholar
• Gotti, F., O’Neil, C. The elasticity of Puiseux monoids. J. Commut Algebra (to appear). [arXiv04207]
   Google Scholar
• Gotti, M. (2019). On the local k-elasticities of Puiseux monoids. Int. J. Algebra Comput. 29(1):147–158. DOI:10.1142/S0218196718500662.
   Web of Science ®Google Scholar
• Grillet, P. A. (2001). Commutative Semigroups, Advances in Mathematics, Vol. 2. Boston: Kluwer Academic Publishers.
   Google Scholar
• Halter-Koch, F. (1984). On the factorization of algebraic integers into irreducibles. Coll. Math. Soc. János Bolyai. 34:699–707.
   Google Scholar
• Kainrath, F. (1999). Factorization in Krull monoids with infinite class group. Colloq. Math. 80(1):23–30. DOI:10.4064/cm-80-1-23-30.
   Google Scholar
• O’Neill, C., Pelayo, R. (2018). Realizable sets of catenary degrees of numerical monoids. Bull. Aust. Math. Soc. 97:240–245. DOI:10.1017/S0004972717000995.
   Web of Science ®Google Scholar
• Narkiewicz, W. (1971). Some unsolved problems. Moires Soc. Math. France 25:159–164. DOI:10.24033/msmf.48.
   Google Scholar
• Narkiewicz, W. (1979). Finite abelian groups and factorization problems. Colloq. Math. 42(1):319–330. DOI:10.4064/cm-42-1-319-330.
   Google Scholar
• Skula, L. (1976). On c-semigroups. ACTA Arith. 31(3):247–257. DOI:10.4064/aa-31-3-247-257.
   Google Scholar
• Tringali, S. Structural properties of subadditive families with applications to factorization theory. Israel J. Math. (to appear). [arXiv03525]
   Web of Science ®Google Scholar
• Valenza, R. (1990). Elasticity of factorization in number fields. J. Number Theory 36(2):212–218. DOI:10.1016/0022-314X(90)90074-2.
   Web of Science ®Google Scholar
• Zaks, A. (1980). Half-factorial domains. Israel J. Math. 37(4):281–302. DOI:10.1007/BF02788927.
   Web of Science ®Google Scholar
• Zhong, Q. On elasticities of locally finitely generated monoids. [arXiv (1807). 11523]
   Google Scholar