@article { author = {Khamechi, Pouyan and Mohammadzadeh Saany, Hossein and Nouri, Leila}, title = {Classification of monoids by Condition $(PWP_{ssc})$}, journal = {Categories and General Algebraic Structures with Applications}, volume = {12}, number = {1}, pages = {175-197}, year = {2020}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {10.29252/cgasa.12.1.175}, abstract = {Condition $(PWP)$ which was introduced in (Laan, V., {\it Pullbacks and flatness properties of acts I}, Commun. Algebra, 29(2) (2001), 829-850), is related to flatness concept of acts over monoids. Golchin and Mohammadzadeh in ({\it On Condition $(PWP_E)$}, Southeast Asian Bull. Math., 33 (2009), 245-256) introduced Condition $(PWP_E)$, such that Condition $(PWP)$ implies it, that is, Condition $(PWP_E)$ is a generalization of Condition $(PWP)$. In this paper we introduce Condition $(PWP_{ssc})$, which is much easier to checkĀ  than Conditions $(PWP)$ and $(PWP_E)$ and does not imply them. Also principally weakly flat is a generalization of this condition. At first, general properties of Condition $(PWP_{ssc})$ will be given. Finally a classification of monoids will be given for which all (cyclic, monocyclic) acts satisfy Condition $(PWP_{ssc})$ and also a classification of monoids $S$ will be given for which all right $S$-acts satisfying some other flatness properties have Condition $(PWP_{ssc})$.}, keywords = {$S$-act,Flatness properties,Condition $(PWP_{ssc})$,semi-cancellative,$e$-cancellative}, url = {https://cgasa.sbu.ac.ir/article_85729.html}, eprint = {https://cgasa.sbu.ac.ir/article_85729_9d3888f3fd18b864c1967d267a21ae2c.pdf} }