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Keywords:
abelian partially ordered groups; partially ordered partial abelian monoids; effect algebras; MV-algebras; Riesz decomposition properties; short exact sequences; extensions
abelian partially ordered groups; partially ordered partial abelian monoids; effect algebras; MV-algebras; Riesz decomposition properties; short exact sequences; extensions
Summary:
The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.
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