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2004•Acta Scientiarum Naturalium Universitatis NeimongolRequires access

Mininjective Modules,Minflat Modules and Some Rings

Zhanmin Zhu

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Abstract

Let R be a ring.A right R-module M is said to be minflat if for every minimal left ideal I the canonical homomorpism M_RI→M_RR is monic.R is called left minhereditary,if every minimal left ideal of R is projective.R is called left minregular,if every minimal left ideal of R is a direct summand.R is called mincoherent,if every minimal left ideal of R is finitely presented.Some characterizations of mininjective modules and minflat modules are given respectively.Minhereditary rings are characterized by mininjective modules,and minregular rings,and mincoherent rings are characterized by mininjective modules and minflat modules.

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What this paper is about

Let R be a ring.A right R-module M is said to be minflat if for every minimal left ideal I the canonical homomorpism M_RI→M_RR is monic.R is called left minhereditary,if every minimal left ideal of R is projective.R is called left minregular,if every minimal left ideal of R is a direct summand.R is called mincoherent,if every minimal left ideal of R is finitely presented.Some characterizations of mininjective modules and minflat modules are given respectively.Minhereditary rings are characterized by mininjective modules,and minregular rings,and mincoherent rings are characterized by mininjective modules and minflat modules.

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Available abstract

Let R be a ring.A right R-module M is said to be minflat if for every minimal left ideal I the canonical homomorpism M_RI→M_RR is monic.R is called left minhereditary,if every minimal left ideal of R is projective.R is called left minregular,if every minimal left ideal of R is a direct summand.R is called mincoherent,if every minimal left ideal of R is finitely presented.Some characterizations of mininjective modules and minflat modules are given respectively.Minhereditary rings are characterized by mininjective modules,and minregular rings,and mincoherent rings are characterized by mininjective modules and minflat modules.

Key concepts: Mathematics, Ideal (ethics), Finitely-generated abelian group, Minimal ideal, Maximal ideal, Flat module, Projective module, Pure mathematics

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