Characterization of monoids by a generalization of weak flatness property

Document Type : Research Paper

Authors

1 Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran

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

10.29252/as.2022.2655

Abstract

In [On a generalization of weak flatness property, Asian-European Journal of Mathematics, 14(1) (2021)] we introduce a generalization of weak flatness property, called $(WF)'$, and showed that a monoid $S$ is absolutely $(WF)'$ if and only if $S$ is regular and satisfies Conditions $(R_{(WF)'})$ and $(L_{(WF)'})$. In this paper we continue the characterization of monoids by this property of their (finitely generated, (mono)cyclic, Rees factor) right acts. Also we give a classification of monoids for which $(WF)'$ property of their (finitely generated, (mono)cyclic, Rees factor) right acts imply other properties and vise versa. The aim of this paper is to show that the class of absolutely $(WF)'$ monoids and absolutely (weakly) flat monids are coincide.

Keywords


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