24
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Arithmetics of flatness for monoids

Received 21 Jul 2023, Accepted 23 Mar 2024, Published online: 06 May 2024

References

  • Angermüller, G. (2017). Unique factorization in torsion-free modules. In: Fontana M., Frisch, S., Glaz, S., Tartarone, F., Zanardo, P., eds. Rings, Polynomials and Modules. Cham: Springer, pp. 13–31.
  • Anderson, D. D., Anderson, D. F., Zafrullah, M. (1990). Factorization in integral domains. J. Pure Appl. Algebra 69:1–19. DOI: 10.1016/0022-4049(90)90074-R.
  • Bulman-Fleming, S. (1999). Flatness properties of acts over commutative cancellative monoids. Mathematika 46:93–102. DOI: 10.1112/S0025579300007592.
  • Dumitrescu, T., Epure, M. (2023). A Schreier type property for modules. J. Algebra Appl. DOI: 10.1142/S0219498824501251.
  • Geroldinger, A., Halter-Koch, F. (1994). Arithmetical theory of monoid homomorphisms. Semigroup Forum 48:333–362. DOI: 10.1007/BF02573682.
  • Geroldinger, A., Halter-Koch, F. (2006). Non-Unique Factorizations. Pure and Applied Mathematics, 278. Chapman and Hall/CRC.
  • Halter-Koch, F. (1998). Ideal Systems. Pure and Applied Mathematics. New York: Marcel Dekker.
  • Howie, J. M. (1995). Fundamentals of Semigroup Theory. London Mathematical Society Monographs New Series. Oxford: Clarendon Press.
  • Jensen, Chr. U. (1966). A remark on flat and projective modules. Can. J. Math. 18:943–949. DOI: 10.4153/CJM-1966-093-7.
  • Kilp, M., Knauer, U., Mikhalev, A. V. (2000). Monoids, Acts and Categories. Expositions in Mathematics 29. Berlin: de Gruyter.
  • Lazard, D. (1969). Autour de la platitude. Bull. Soc. Math. France 97:81–128. DOI: 10.24033/bsmf.1675.
  • Nicolas, A.-M. (1974). Extensions factorielles et modules factorables. Bull. Sc. math. 2e série 98:117–143.
  • Richman, F. (1965). Generalized quotient rings. Proc. Amer. Math. Soc. 16:794–799. DOI: 10.2307/2033925.
  • Stenström, B. (1971). Flatness and localization of monoids. Math. Nachrichten 48:315–333 DOI: 10.1002/mana.19710480124.
  • Zafrullah, M. (1987). On a property of pre-Schreier domains. Commun. Algebra 15(9):1895–1920. DOI: 10.1080/00927878708823512.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.