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Bases of minimal elements of some partially ordered free abelian groups

Pavel Příhoda (2003)

Commentationes Mathematicae Universitatis Carolinae

In the present paper, we will show that the set of minimal elements of a full affine semigroup A 0 k contains a free basis of the group generated by A in k . This will be applied to the study of the group K 0 ( R ) for a semilocal ring R .

Behavior of countably generated pure-projective modules.

Goro Azumaya (1992)

Publicacions Matemàtiques

We first prove that every countably presented module is a pure epimorphic image of a countably generated pure-projective module, and by using this we prove that if every countably generated pure-projective module is pure-injective then every module is pure-injective, while if in any countably generated pure-projective module every countably generated pure-projective pure submodule is a direct summand then every module is pure-projective.

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