journal6 ›› 2002, Vol. 23 ›› Issue (1): 55-56.

• Mathematics • Previous Articles     Next Articles

On Quasi-projective System


  1. (Dept.of Math.,Hubei Institute for Nationalities,Enshi 445000,Hubei China)
  • Online:2002-03-15 Published:2013-01-05

Abstract: Let S  be a monoid,A  is quasi-projective S -system if for every S -epimophism f:A→B and S-homomorphism g:A→B,there exists a S-homomorphism h:A→A such that fh=g.The properties of quasi-projective S -system are studied and two main results are obtained:(1) S is a(semi) perfect monoid if and only if for every (f.g.) right S-system have a quasi-projective cover S -system;(2) S is a right hereditary monoid if and only if every projective S -systemis quasi-projective.

Key words: projective system, quasi-projective system, (semi)perfect monoids, hereditary monoids

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