Geodesic
Generalizations of pseudo MV-algebras and generalized pseudo effect algebras
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 395-415

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We deal with unbounded dually residuated lattices that generalize pseudo $MV$-algebras in such a way that every principal order-ideal is a pseudo $MV$-algebra. We describe the connections of these generalized pseudo $MV$-algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo $MV$-algebra $A$ by means of the positive cone of a suitable $\ell $-group $G_A$. We prove that the lattice of all (normal) ideals of $A$ and the lattice of all (normal) convex $\ell $-subgroups of $G_A$ are isomorphic. We also introduce the concept of Archimedeanness and show that every Archimedean generalized pseudo $MV$-algebra is commutative.
Classification : 03G25, 06F05
Keywords: pseudo $MV$-algebra; $DR\ell $-monoid; generalized pseudo effect algebra 
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     author = {K\"uhr, Jan},
     title = {Generalizations of pseudo {MV-algebras} and generalized pseudo effect algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {395--415},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
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     zbl = {1174.06330},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008__58_2_a6/}
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Kühr, Jan. Generalizations of pseudo MV-algebras and generalized pseudo effect algebras. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 395-415. http://geodesic.mathdoc.fr/item/CMJ_2008__58_2_a6/