On a generalization of condition (PWP)

Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎Lanzhou University‎, ‎Lanzhou‎, ‎Gansu 730000‎, ‎P.R. China.‎ ‎

2 Department of Mathematics‎, ‎Lanzhou University‎, ‎Lanzhou‎, ‎Gansu 730000‎, ‎P.R. China.

Abstract

‎There is a flatness property of acts over monoids called Condition $(PWP)$ which‎, ‎so far‎, ‎has received‎ ‎much attention‎. ‎In this paper‎, ‎we introduce Condition GP-$(P)$‎, ‎which is a generalization of Condition $(PWP)$‎. ‎Firstly‎, ‎some  characterizations of monoids by Condition GP-$(P)$ of their‎ ‎(cyclic‎, ‎Rees factor) acts are given‎, ‎and many known results are generalized‎. ‎Moreover‎, ‎some possible conditions on monoids that describe when their diagonal acts satisfy Condition GP-$(P)$ are found‎. ‎Finally‎, ‎using some new types of epimorphisms‎, ‎an alternative description of Condition GP-$(P)$ (resp.‎, ‎Condition $(PWP)$) is obtained‎, ‎and directed‎ ‎colimits of these new epimorphisms are investigated.

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Main Subjects


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Volume 42, Issue 5
September and October 2016
Pages 1057-1076
  • Receive Date: 16 January 2015
  • Revise Date: 23 June 2015
  • Accept Date: 23 June 2015