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On idempotent modifications of generalized $MV$-algebras

In: Mathematica Slovaca, vol. 60, no. 2
Ján Jakubík
Detaily:
Rok, strany: 2010, 179 - 188
Kľúčové slová:
generalized MV-algebra, lattice ordered group, direct irreducibility, subdirect irreducibility, boolean element
O článku:
The notion of idempotent modification of an algebra was introduced by Ježek; he proved that the idempotent modification of a group is always subdirectly irreducible. In the present note we show that the idempotent modification of a generalized $MV$-algebra having more than two elements is directly irreducible if and only if there exists an element in $\mathcal A$ which fails to be boolean. Some further results on idempotent modifications are also proved.
Ako citovať:
ISO 690:
Jakubík, J. 2010. On idempotent modifications of generalized $MV$-algebras. In Mathematica Slovaca, vol. 60, no.2, pp. 179-188. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0004-z

APA:
Jakubík, J. (2010). On idempotent modifications of generalized $MV$-algebras. Mathematica Slovaca, 60(2), 179-188. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0004-z
O vydaní: