On half-factoriality of transfer Krull monoids

References

• Adams, D., Ardila, R., Hannasch, D., Kosh, A., McCarthy, H., Ponomarenko, V., Rosenbaum, R. (2009). Bifurcus semigroups and rings. Involve. 2(3):351–356. DOI: 10.2140/involve.2009.2.351.
   Google Scholar
• Baeth, N. R., Smertnig, D. (2015). Factorization theory: from commutative to noncommutative settings. J. Algebra 441:475–551. DOI: 10.1016/j.jalgebra.2015.06.007.
   Web of Science ®Google Scholar
• Baginski, P., Kravitz, R. (2010). A new characterization of half-factorial Krull monoids. J. Algebra Appl. 09(05):825–837. DOI: 10.1142/S0219498810004269.
   Web of Science ®Google Scholar
• Carlitz, L. (1960). A characterization of algebraic number fields with class number two. Proc. Am. Math. Soc. 11:291–392.
   Google Scholar
• Chapman, S. T., Coykendall, J. (2000). Half-factorial domains, a survey. In: Non-Noetherian Commutative Ring Theory, Mathematics and Its Applications, Vol. 520, Boston, MA: Kluwer Academic Publishers, pp. 97–115.
   Google Scholar
• Chapman, S. T., Krause, U., Oeljeklaus, E. (2000). Monoids determined by a homogeneous linear diophantine equation and the half-factorial property. J. Pure Appl. Algebra 151(2):107–133. DOI: 10.1016/S0022-4049(99)00062-6.
   Web of Science ®Google Scholar
• Coykendall, J. (2005). Extensions of half-factorial domains: A survey. In: Arithmetical Properties of Commutative Rings and Monoids, Lect. Notes Pure Appl. Math., Vol. 241. Boca Raton, FL: Chapman & Hall/CRC, pp. 46–70.
   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. 16(12):1750234–1750242. DOI: 10.1142/S0219498817502346.
   Web of Science ®Google Scholar
• Fan, Y., Tringali, S. (2018). Power monoids: A bridge between factorization theory and arithmetic combinatorics. J. Algebra 512:252–294. DOI: 10.1016/j.jalgebra.2018.07.010.
   Web of Science ®Google Scholar
• Geroldinger, A. (2016). Sets of lengths. Amer. Math. Mon. 123:960–988.
   Web of Science ®Google Scholar
• Geroldinger, A., Göbel, R. (2003). Half-factorial subsets in infinite abelian groups. Houst. J. Math. 29:841–858.
   Web of Science ®Google Scholar
• Geroldinger, A., Halter-Koch, F. (2006). Non-unique factorizations. In: Algebraic, Combinatorial and Analytic Theory, Pure and Applied Mathematics, Vol. 278, Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Geroldinger, A., Kainrath, F., Reinhart, A. (2015). Arithmetic of seminormal weakly Krull monoids and domains. J. Algebra 444:201–245. DOI: 10.1016/j.jalgebra.2015.07.026.
   Web of Science ®Google Scholar
• Geroldinger, A., Reinhart, A. (2019). The monotone catenary degree of monoids of ideals. Int. J. Algebra Comput. 29(03):419–457. DOI: 10.1142/S0218196719500097.
   Google Scholar
• Geroldinger, A., Zhong, Q. (2016). The set of minimal distances in Krull monoids. Acta Arith. 173:1–120. DOI: 10.4064/aa7906-1-2016.
   Web of Science ®Google Scholar
• Geroldinger, A., Zhong, Q. (2020). Factorization theory in commutative monoids. Semigroup Forum. 100(1):22–51. DOI: 10.1007/s00233-019-10079-0.
   Web of Science ®Google Scholar
• Gotti, F. (2020). Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid. Linear Algebra Appl. 604:146–186. DOI: 10.1016/j.laa.2020.06.009.
   Web of Science ®Google Scholar
• Kainrath, F., Lettl, G. (2000). Geometric notes on monoids. Semigroup Forum. 61(2):298–302. DOI: 10.1007/PL00006026.
   Web of Science ®Google Scholar
• Malcolmson, P., Okoh, F. (2009). Power series extensions of half-factorial domains. J. Pure Appl. Algebra 213(4):493–495. DOI: 10.1016/j.jpaa.2008.07.014.
   Web of Science ®Google Scholar
• Malcolmson, P., Okoh, F. (2016). Half-factorial subrings of factorial domains. J. Pure Appl. Algebra 220(3):877–891. DOI: 10.1016/j.jpaa.2015.06.011.
   Web of Science ®Google Scholar
• Plagne, A., Schmid, W. A. (2005). On large half-factorial sets in elementary p-groups: maximal cardinality and structural characterization. Isr. J. Math. 145(1):285–310. DOI: 10.1007/BF02786695.
   Google Scholar
• Plagne, A., Schmid, W. A. (2005). On the maximal cardinality of half-factorial sets in cyclic groups. Math. Ann. 333(4):759–785. DOI: 10.1007/s00208-005-0690-y.
   Web of Science ®Google Scholar
• Roitman, M. (2011). A quasi-local half-factorial domain with an atomic non-half-factorial integral closure. J. Commut. Algebra 3(3):431–438. DOI: 10.1216/JCA-2011-3-3-431.
   Web of Science ®Google Scholar
• Schmid, W. A. (2005). Differences in sets of lengths of Krull monoids with finite class group. J. Théor. Nombres Bordeaux. 17(1):323–345. DOI: 10.5802/jtnb.493.
   Google Scholar
• Schmid, W. A. (2005). Half-factorial sets in finite abelian groups: a survey. Grazer Math. Ber. 348:41–64.
   Google Scholar
• Schmid, W. A. (2006). Half-factorial sets in elementary p-groups. Far East J. Math. Sci. 22:75–114.
   Google Scholar
• Schmid, W. A. (2009). Arithmetical characterization of class groups of the form Z/nZ⊕Z/nZ via the system of sets of lengths. Abh. Math. Semin. Univ. Hamb. 79:25–35.
   Web of Science ®Google Scholar
• Skula, L. (1976). On c-semigroups. Acta Arith. 31(3):247–257. DOI: 10.4064/aa-31-3-247-257.
   Google Scholar
• Śliwa, J. (1976). Factorizations of distinct lengths in algebraic number fields. Acta Arith. 31(4):399–417. DOI: 10.4064/aa-31-4-399-417.
   Google Scholar
• Smertnig, D. (2019). Factorizations in bounded hereditary noetherian prime rings. Proc. Edinb. Math. Soc. 62(2):395–442. DOI: 10.1017/S0013091518000305.
   Web of Science ®Google Scholar
• Smertnig, D. (2013). Sets of lengths in maximal orders in central simple algebras. J. Algebra 390:1–43. DOI: 10.1016/j.jalgebra.2013.05.016.
   PubMed Web of Science ®Google Scholar
• Zaks, A. (1976). Half factorial domains. Bull. Amer. Math. Soc. 82(5):721–723. DOI: 10.1090/S0002-9904-1976-14130-4.
   Web of Science ®Google Scholar
• Zaks, A. (1980). Half-factorial-domains. Isr. J. Math. 37(4):281–302. DOI: 10.1007/BF02788927.
   Web of Science ®Google Scholar