Displaying similar documents to “Bases of minimal elements of some partially ordered free abelian groups”

On the embedding of ordered semigroups into ordered group

Mohammed Ali Faya Ibrahim (2004)

Czechoslovak Mathematical Journal

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It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of L -maher and R -maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered L or R -maher semigroup can be embedded into an ordered...

Some properties of Lorenzen ideal systems

Aleka Kalapodi, Angeliki Kontolatou, Jiří Močkoř (2000)

Archivum Mathematicum

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Let G be a partially ordered abelian group ( p o -group). The construction of the Lorenzen ideal r a -system in G is investigated and the functorial properties of this construction with respect to the semigroup ( R ( G ) , ⊕ , ≤ ) of all r -ideal systems defined on G are derived, where for r , s ∈ R ( G ) and a lower bounded subset X ⊆ G , X r ⊕ s = X r ∩ X s . It is proved that Lorenzen construction is the natural transformation between two functors from the category of p o -groups with special morphisms into the category of abelian ordered semigroups. ...

Homomorphisms between A -projective Abelian groups and left Kasch-rings

Ulrich F. Albrecht, Jong-Woo Jeong (1998)

Czechoslovak Mathematical Journal

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Glaz and Wickless introduced the class G of mixed abelian groups A which have finite torsion-free rank and satisfy the following three properties: i) A p is finite for all primes p , ii) A is isomorphic to a pure subgroup of Π p A p , and iii) H o m ( A , t A ) is torsion. A ring R is a left Kasch ring if every proper right ideal of R has a non-zero left annihilator. We characterize the elements A of G such that E ( A ) / t E ( A ) is a left Kasch ring, and discuss related results.