Abstract
In this paper we introduce the concept of weakly left cancellative semirings. Moreover we establish a connection between commutativity for this class of semirings and derivations.
Similar content being viewed by others
References
Allen, P.J.: A fundamental theorem of homomorphisms for semirings. Proc. Am. Math. Soc. 21, 412–416 (1969)
Bell, H.E., Daif, M.N.: On derivations and commutativity in prime rings. Acta Math. Hung. 66, 337–343 (1995)
Bell, H.E., Daif, M.N.: Remarks on derivations on semiprime rings. Int. J. Math. Math. Sci. 15, 205–206 (1992)
Dedekind, R.: Über die Theorie der ganzen algebraiscen Zahlen. D: Druck und Verlag, Braunschweig (1894)
Golan, J.S.: Semirings and Their Applications. Kluwer Academic Publishers, Dordrecht (1999)
Gupta, V., Chaudhari, J.N.: On commutativity of semirings. East West J. Math. 8, 97–100 (2006)
Hongan, M.: A note on semiprime rings with derivation. Int. J. Math. Math. Sci. 20, 413–415 (1997)
Posner, E.C.: Derivations in prime rings. Proc. Am. Math. Soc. 8, 1093–1100 (1957)
Sardar, S.K.: On derivation in semirings. Southeast Asian Bull. Math. 33, 917–928 (2009)
Shabir, M., Ali, A., Batool, S.: A note on quasi-ideals in semirings. Southeast Asian Bull. Math. 27(5), 923–928 (2004)
Vandiver, H.S.: Note on a simple type of algebra in which the cancellation law of addition does not hold. Bull. Am. Math. Soc. 40(12), 914–920 (1934)
Yazarli, H., Öztürk, M.A.: On the centroid of prime semirings. Turk. J. Math. 37, 577–584 (2013)
Weinert, H.J.: Über Halbringe und Halbkörper I. Acta Math. Hung. 13, 365–378 (1962)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
DE Filippis, V., Mamouni, A. & Oukhtite, L. Weakly left cancellative semirings with derivations. São Paulo J. Math. Sci. 14, 351–360 (2020). https://doi.org/10.1007/s40863-019-00148-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40863-019-00148-1