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Paper
Title

On GPW-Flat Acts

Year: 1399
COI: JR_CGASAT-12-1_002
Language: EnglishView: 20
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Authors

Hamideh Rashidi - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
Akbar Golchin - University of Sistan and Baluchestan
Hossein Mohammadzadeh Saany - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract:

In this article, we present GPW-flatness property of acts over monoids, which is a generalization of principal weak flatness. We say that a right S-act A_{S} is GPW-flat if for every s \in S, there exists a natural number n = n_ {(s, A_{S})} \in \mathbb{N} such that the functor A_{S} \otimes {}_{S}- preserves the embedding of the principal left ideal {}_{S}(Ss^n) into {}_{S}S. We show that a right S-act A_{S} is GPW-flat if and only if for every s \in S there exists a natural number n = n_{(s, A_{S})} \in \mathbb{N} such that the corresponding \varphi is surjective for the pullback diagram P(Ss^n, Ss^n, \iota, \iota, S), where \iota : {}_{S}(Ss^n) \rightarrow {}_{S}S is a monomorphism of left S-acts. Also we give some general properties and a characterization of monoids for which this condition of their acts implies some other properties and vice versa.

Keywords:

GPW-flat , Eventually regular monoid , Eventually left almost regular monoid

Paper COI Code

This Paper COI Code is JR_CGASAT-12-1_002. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1267945/

How to Cite to This Paper:

If you want to refer to this Paper in your research work, you can simply use the following phrase in the resources section:
Rashidi, Hamideh and Golchin, Akbar and Mohammadzadeh Saany, Hossein,1399,On GPW-Flat Acts,https://civilica.com/doc/1267945

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  • Bulman-Fleming, S., Kilp, M., and Laan, V., Pullbacks and flatness ...
  • Golchin, A., Flatness and coproducts, Semigroup Forum ۷۲(۳) (۲۰۰۶), ۴۳۳-۴۴۰ ...
  • Golchin, A., On flatness of acts, Semigroup Forum ۶۷(۲) (۲۰۰۳), ...
  • Golchin, A. and Mohammadzadeh, H., On Condition (P۰), Semigroup Forum ...
  • Golchin, A. and Mohammadzadeh, H., On regularity of Acts, J. ...
  • Golchin, A., Zare, A., and Mohammadzadeh, H., E-torsion free acts ...
  • Kilp, M., On flat acts (Russian), Tatru UL. Toimetisted, ۲۵۳ ...
  • Kilp, M., Characterization of monoids by properties of their left ...
  • Kilp, M., Knauer, U., and Mikhalev, A., “Monoids, Acts and ...
  • Laan, V., Pullbacks and flatness properties of acts I., Comm. ...
  • Nouri, L., Golchin, A., and Mohammadzadeh, H., On properties of ...
  • Qiao, H., Some new characterizations of right cancellative monoids by ...
  • Qiao, H., Limin, W., and Zhongkui, L., On some new ...
  • Sedaghatjoo, M., Khosravi, R., and Ershad, M., Principally weakly and ...
  • Zare, A., Golchin, A., and Mohammadzadeh, H., Strongly torsion free ...
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