Characterization of monoids by ($U$-)$GPW$-flatness of right acts

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran

2 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

The authors in 2020 introduced $GPW$-flatness and gave a characterization of monoids by this property of their right acts. In this article we continue this investigation and will give a characterization of monoids by this condition of their right Rees factor acts. Also we give a characterization of monoids by comparing this property of their  right acts with other properties.
We also introduce $U$-$GPW$-flatness of acts, which is an extension of $GPW$-flatness and give some general properties and a characterization of monoids when this property of acts implies some others and vice versa. 

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Main Subjects

References

[1] Arabtash, M., Golchin, A., and Mohammadzadeh, H., On Condition (G − PWP), Categ. Gen. Algebr. Struct. Appl. 5(1) (2016), 55-84.
[2] Bulman-Fleming, S., Kilp, M., and Laan, V., Pullbacks and flatness properties of acts II, Comm. Algebra 29(2) (2001), 851-878.
[3] Golchin, A. and Mohammadzadeh, H., On Condition (PWPE), Southeast Asian Bull. Math. 33 (2009), 245-256.
[4] Golchin, A. and Mohammadzadeh, H., On homological classification of monoids by Condition (PE) of right acts, Ital. J. Pure Appl. Math. 25 (2009), 175-186.
[5] Golchin, A. and Mohammadzadeh, H., On regularity of Acts, J. Sci. I. R. Iran 19(4) (2008), 339-345.
[6] Golchin, A. and Mohammadzadeh, H., On Condition (EP), Int. Math. Forum 2(19) (2007), 911-918.
[7] Golchin, A. and Mohammadzadeh, H., On Condition (E′P), J. Sci. I. R. Iran 17(4) (2006), 343-349.
[8] Golchin, A., Mohammadzade, H., and Rezaei, P., On P-regularity of acts, Adv. Pure Math. 2(02) (2012), 104-108.
[9] Golchin, A., Rezaei, P., and Mohammadzadeh, H., On Strongly (P)-cyclic acts, Czechoslov. Math. J. 59(314) (2009), 595-611.
[10] Kilp, M., On flat acts (Russian), Tatru UL. Toimetisted 253 (1970), 66-72.
[11] Kilp, M., Characterization of monoids by properties of their left Rees factors, Tatru UL. Toimetisted, 640 (1983), 29-37.
[12] Kilp, M., Knauer, U., and Mikhalev, A., “Monoids, Acts and Categories with Application to Wreath Products and Graphs”, A Handbook for Students and Researchers, Walter de Gruyter, 2000.
[13] Laan, V., Pullbacks and flatness properties of acts, Ph.D. Thesis, Tartu, 1999.
[14] Qiao, H. and Wei, Ch., On a generalization of principal weak flatness property, Semigroup Forum 85(2) (2012), 147-159.
[15] Rashidi, H., Golchin, A., and Mohammadzadeh Saany, H., On GPW-flat acts, Categ. Gen. Algebr. Struct. Appl. 12(1) (2020), 175-197.
[16] Zare, A., Golchin, A., and Mohammadzadeh, H., Strongly torsion free acts over monoids, Asian-Eur. J. Math. 6(3) (2013), 1350049 (22pages).
[17] Zare, A., Golchin, A., and Mohammadzadeh, H., R-torsion free acts over monoids,
J. Sci. I. R. Iran 24(3) (2013), 275–286.
Categories and General Algebraic Structures with Applications
Volume 21, Issue 1
July 2024
Pages 127-152

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