Some Conditions on Monoids for Which Condition (P) Acts Are Strongly Flat

Abstract

Strong flatness and condition (P) property of right S-acts over a monoid S have been the topic of many papers on homological classification of monoids. In this paper, we continue to investigate the monoids over which every right S-act satisfying condition (P) is strongly flat and we obtain some new classes of monoids.

Key Words:

• Condition (P)
• Strong flatness
• Homological classification

Mathematics Subject Classification:

• 20M30
• 18G05
• 06F05

Acknowledgments

The author would like to thank the anonymous referee for useful comments to an earlier draft of this paper and for improving the proof of Theorem 2.3 and Theorem 2.9. He would also like to thank Professor P. M. Higgins for suggestions which lent great clarity to the exposition of this work. Research supported by National Natural Science Foundation of China(10171082) and by NWNU-KJCXGC212.

Notes

^#Communicated by P. Higgins.