Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2020; 35(3): 697-709

Online first article April 8, 2020      Printed July 31, 2020

https://doi.org/10.4134/CKMS.c190317

Copyright © The Korean Mathematical Society.

Classifying monoids by quasi-annihilator (homo)flatness of their right Rees factors

Reza Aminizadeh, Hamid Rasouli, Abolfazl Tehranian

Islamic Azad University; Islamic Azad University; Islamic Azad University

Abstract

In this paper, the class of quasi-annihilator (homo)flat acts based on the notion of quasi-annihilator ideal is introduced. This class lies strictly between the classes of weakly (homo)flat and principally weakly (homo)flat acts. Some properties of such kinds of flatness are studied. We present some homological classifications for monoids by means of quasi-annihilator (homo)flatness of their right Rees factor acts.

Keywords: $S$-act, quasi-annihilator ideal, quasi-annihilator (homo)flat act, quasi-annihilator ideally connected monoid

MSC numbers: 20M30, 20M50, 18B40

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