On Condition (G-PWP) | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 3، دوره 5، شماره 1، مهر 2016، صفحه 55-84 اصل مقاله (240.64 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Mostafa Arabtash؛ Akbar Golchin؛ Hossein Mohammadzadeh Saany | ||
| Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran. | ||
| چکیده | ||
| Laan in (Ph.D Thesis, Tartu. 1999) introduced the principal weak form of Condition $(P)$ as Condition $(PWP)$ and gave some characterization of monoids by this condition of their acts. In this paper first we introduce Condition (G-PWP), a generalization of Condition $(PWP)$ of acts over monoids and then will give a characterization of monoids when all right acts satisfy this condition. We also give a characterization of monoids, by comparing this property of their acts with some others. Finally, we give a characterization of monoids coming from some special classes, by this property of their diagonal acts and extend some results on Condition $(PWP)$ to this condition of acts. | ||
| کلیدواژهها | ||
| $S$-act؛ condition ($PWP$)؛ condition ($G$-$PWP$) | ||
| مراجع | ||
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[1] A. Golchin and H. Mohammadzadeh, On Condition (EP), Int. Math. Forum 19 (2007), 911-918. [2] A. Golchin and H. Mohammadzadeh, On Condition (E0P), J. Sci. Islam. Repub. Iran 17(4) (2006), 343-349. [3] A. Golchin and H. Mohammadzadeh, On Condition (PWPE), Southeast Asian Bull. Math. 33 (2009), 245-256. [4] A. Golchin and H. Mohammadzadeh, On Condition (P0), Semigroup Forum 86 (2013), 413-430. [5] J.M. Howie, Fundamentals of Semigroup Theory", London Mathematical Society Monographs. Oxford University Press, London, 1995. [6] Q. Husheng, Some new characterization of right cancellative monoids by Condition (PWP), Semigroup Forum 71 (2005), 134-139. [7] Q. Husheng and W. Chongqing, On a generalization of principal weak flatness property, Semigroup Forum 85 (2012), 147-159. [8] M. Kilp, U. Knauer, and A. Mikhalev, Monoids, Acts and Categories", Berlin: W. De Gruyter, 2000. [9] V. Laan, On a generalization of strong flatness, Acta Comment. Univ. Tartu Math 2 (1998), 55-60. [10] V. Laan, Pullbacks and flatness properties of acts", Ph.D. Thesis, Tartu. 1999. [11] V. Laan, Pullbacks and flatness properties of acts II, Comm. Algebra 29(2) (2001), 851-878. [12] B. Stenstrom, Flatness and localization over monoids. Math. Nachr. 48 (1971), 315-334. [13] P. Normak, On equalizer-flat and pullback-flat acts. Semigroup Forum 36 (1987), 293-313. [14] A. Zare, A. Golchin, and H. Mohammadzadeh, Strongly torsion free acts over monoids, Asian-Eur. J. Math. 6(3) (2013), 22 pages. | ||
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