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

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.

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References

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Algebraic Structures and Their Applications
Volume 9, Issue 2
August 2022
Pages 57-75

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