On P-Regularity of Acts

Abstract

By a regular act we mean an act that all its cyclic subacts are projective. In this paper we introduce P-regularity of acts over monoids and will give a characterization of monoids by this property of their right (Rees factor) acts.

Share and Cite:

A. Golchin, H. Mohammadzadeh and P. Rezaei, "On P-Regularity of Acts," Advances in Pure Mathematics, Vol. 2 No. 2, 2012, pp. 104-108. doi: 10.4236/apm.2012.22014.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] J. M. Howie, “Fundamentals of Semigroup Theory,” Clarendon Press, Oxford, 1995.
[2] M. Kilp, U. Knauer and A. Mikhalev, “Monoids, Acts and Categories,” W. de Gruyter, Berlin, 2000. doi:10.1515/9783110812909
[3] V. Laan, “Pullbacks and Flatness Properties of Acts,” Tartu University Press, Tartu, 1999.
[4] V. Laan, “Pullbacks and Flatness Properties of Acts I,” Communications in Algebra, Vol. 29, No. 2, 2001, pp. 829- 850. doi:10.1081/AGB-100001547
[5] P. Normak, “Analogies of QF-Ring for Monoids. I,” Tartu ülikooli Toimetised, Vol. 556, 1981, pp. 38-46.
[6] S. Bulman-Fleming, M. Kilp and V. Laan, “Pullbacks and Flatness Properties of Acts II,” Communications in Algebra, Vol. 29, No. 2, 2001, pp. 851-878. doi:10.1081/AGB-100001548

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.