Characterization of Monoids by a Generalization of Flatness Property

It is well-known that, using principal weak flatness property, some important monoids are characterized, such as regular monoids, left almost regular monoids, and so on. In this article, we define a generalization of principal weak flatness called GP-Flatness, and will characterize monoids by this property of their right (Rees factor) acts. Also we investigate new classes of monoids called generally regular monoids and generally left almost regular monoids.

Authors:

• Mahdiyeh Abbasi
• Akbar Golchin

Keywords:

• G-left stabilizing
• GP-flatness
• generally regular
• principal weak flatness.

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