Abstract

AbstractIn this survey we give an account of the relationships between \(\ell \)-groups and some important algebraic structures like MV-algebras, BL-algebras, and their non-commutative versions given by pseudo MV-algebras and pseudo BL-algebras. In a similar way we show how partially ordered groups are connected with quantum structures like orthomodular lattices, effect algebras and pseudo effect algebras. For the latter classes, an important role is played by various types of the Riesz Decomposition Property.KeywordsMV-algebraEffect algebra \(\ell \)-groupPo-groupStrong unitUnital po-groupBL-algebraPseudo MV-algebraPseudo BL-algebraKite

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