Abstract
The concepts of weakly injective, fg-weakly injective, and p-weakly injective S-acts generalize that of injective S-act. We study the monoids S over which the classes of weakly injective, fg-weakly injective, and p-weakly injective S-acts are axiomatizable. We prove that the class of p-weakly injective S-acts over a regular monoid is axiomatizable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Gould V., Mikhalev A. V., Palyutin E. A., and Stepanova A. A., “Model-theoretic properties of free, projective, and flat S-acts,” J. Math. Sci. (New York), vol. 164, no. 2, 195–227 (2010).
Stepanova A. A., “Axiomatizability and completeness of some classes of S-polygons,” Algebra and Logic, vol. 30, no. 5, 379–388 (1991).
Gould V., “Axiomatisability problems for S-systems,” J. London Math. Soc., vol. 35, 193–201 (1987).
Mikhalev A. V., Ovchinnikova E. V., Palyutin E. A., and Stepanova A. A., “Model-theoretic properties of regular polygons,” J. Math. Sci. (New York), vol. 140, no. 2, 250–285 (2007).
Stepanova A. A., “Axiomatizability and model completeness of the class of regular polygons,” Sib. Math. J., vol. 35, no. 1, 166–177 (1994).
Stepanova A. A., “Axiomatizability and completeness of the class of injective acts over a commutative monoid or a group,” Sib. Math. J., vol. 56, no. 3, 516–525 (2015).
Kasch F., Modules and Rings [Russian translation], Mir, Moscow (1981).
Berthiaume P., “The injective envelope of S-sets,” Bull. Amer. Math. Soc., vol. 10, 261–273 (1967).
Gould V., “The characterization of monoids by properties of their S-systems,” Semigroup Forum, vol. 32, 251–265 (1985).
Luedeman J., McMorris F., and Sim S.-K., “Semigroups for which every totally irreducible S-system is injective,” Comment. Math. Univ. Carolinae, vol. 19, 27–35 (1978).
Kilp M., Knauer U., and Mikhalev A. V., Monoids, Acts and Categories with Applications to Wreath Products and Graphs: A Handbook for Students and Researchers, De Gruyter, Berlin and New York (2000).
Malcev A. I., Algebraic Systems, Springer-Verlag and Akademie-Verlag, Berlin, Heidelberg, and New York (1973).
Ershov Yu. L. and Palyutin E. A., Mathematical Logic [Russian], Nauka, Moscow (1987).
Chang C. C. and Keisler H. J., Model Theory, North-Holland, Amsterdam and London (1973).
Author information
Authors and Affiliations
Corresponding author
Additional information
Vladivostok. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 4, pp. 785–795, July–August, 2017
Rights and permissions
About this article
Cite this article
Efremov, E.L., Stepanova, A.A. Axiomatizability of the class of weakly injective S-acts. Sib Math J 58, 611–618 (2017). https://doi.org/10.1134/S0037446617040073
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446617040073