CLASSIFICATION OF MONOIDS BY CONDITION (GPWPsec) OF RIGHT ACTS

Document Type : Original Manuscript

Authors

Department of Mathematics, Sistan and Baluchestan University, P.O. Box 987-98155, Zahedan, Iran.

10.22044/jas.2024.14066.1800

Abstract

In (Categories and General Algebraic
Structures with Applications, 12(1):175-197 (2020)), Rashidi et al. introduced GPW-flatness
of acts over monoids as a generalization of principal
weak flatness.
In this paper, we introduce Condition (GPWPsec) of acts over
monoids and compare it with GPW-flatness. Also, we obtain
some general properties of Condition (GPWPsec) and characterize
those monoids for which this condition implies some other
properties and vice versa.


در( رسته ها و ساختارهای جبری عمومی با کاربردها 12(1):175-197(2020))، رشیدی و همکاران خاصیت
همواری - GPW
سیستم ها روی تکواره ها را به عنوان تعمیمی از به طور اساسی ضعیف همواری معرفی کردند. در این مقاله شرط
(〖GPWP〗_sec)
از سیستم ها روی تکواره ها را ارائه و آن را با
همواری - GPW
مقایسه می کنیم. همچنین برخی از خواص کلی شرط
(〖GPWP〗_sec)
. را به دست می آوریم و به دسته بندی تکوارهایی خواهیم پرداخت که این شرط سایر خواص را نتیجه دهد و برعکس

Keywords

References

1. S. Bulman-Fleming and A. Gilmour, Flatness properties of diagonal acts over monoids, Semigroup Forum, 76 (2009), 298–314.
 
2. S. Bulman-Fleming, M. Kilp and V. Laan, Pullbacks and flatness properties of acts II, Comm. Algebra, 29 (2001), 851–878.
 
3. A. Golchin, On flatness of acts, Semigroup Forum, 67 (2003), 262–270.
 
4. A. Golchin and H. Mohammadzadeh Saany, Condition (EP), Int. Math. Forum, 2 (2007), 911–918.
 
5. A. Golchin and H. Mohammadzadeh Saany, Condition (E′P), J. Sci. Islam. Repub. Iran, 7 (2006), 343–349.
 
6. J. M. Howie, Fundamentals of Semigroup Theory, London Mathematical Society Monographs, OUP, 1995.
 
7. P. Khamechi, H. Mohammadzadeh Saany and L. Nouri, Classification of monoids by Condition (PWPssc) of right acts, Categ. Gen. Algebr. Struct. Appl., 12 (2020), 175–197.
 
8. M. Kilp, U. Knauer and A. Mikhalev, Monoids, Acts and Categories, W. De Gruyter, Berlin, 2000.
 
9. V. Laan, Pullbacks and flatness properties of atcs, PhD Thesis, Tartu, 1999.
 
10. V. Laan, Pullbacks and flatness properties of acts I, Comm. Algebra, 29 (2001), 829–850.
 
11. H. Rashidi, A. Golchin and H. Mohammadzadeh Saany, On GPW-flat acts, Categ. Gen. Algebr. Struct. Appl., 12 (2020), 175–197. 
 
 12. A. Zare, A. Golchin and H. Mohammadzdeh, R-torsion free acts over monoids, J. Sci. Islam. Repub. Iran, 24 (2013), 275–285. 
Journal of Algebraic Systems
Volume 14, Issue 2
April 2026
Pages 343-367

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