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Title: Generalizations of pseudo MV-algebras and generalized pseudo effect algebras (English)
Author: Kühr, Jan
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 2
Year: 2008
Pages: 395-415
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: pseudo $MV$-algebra
Keyword: $DR\ell $-monoid
Keyword: generalized pseudo effect algebra
MSC: 03G25
MSC: 06F05
idZBL: Zbl 1174.06330
idMR: MR2411097
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Date available: 2009-09-24T11:55:34Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/128265
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