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On a generalization of weak flatness

Authors: Akbar Golchin; Mahdiyeh Abbasi; Hossein Mohammadzadeh Saany;

On a generalization of weak flatness

Abstract

Laan in Pullbacks and flatness properties of acts I, [Commun. Algebra 29(2) (2001) 829–850] introduced Condition [Formula: see text], a generalization of Condition [Formula: see text]. Golchin and Mohammadzadeh in [On Condition ([Formula: see text]), Semigroup Forum 86(2) (2012) 413–430] introduced Condition [Formula: see text], a generalization of Condition [Formula: see text]. In this paper similarly, we introduce a generalization of weak flatness property, called [Formula: see text], and will classify monoids by this property of their acts. We also characterize [Formula: see text] coherent monoids in general and monoids coming from some special classes.

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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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