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Nearly disjoint sequences in convergence l -groups

Ján Jakubík (2000)

Mathematica Bohemica

For an abelian lattice ordered group G let G be the system of all compatible convergences on G ; this system is a meet semilattice but in general it fails to be a lattice. Let α n d be the convergence on G which is generated by the set of all nearly disjoint sequences in G , and let α be any element of G . In the present paper we prove that the join α n d α does exist in G .

Normalization of M V -algebras

Ivan Chajda, Radomír Halaš, Jan Kühr, Alena Vanžurová (2005)

Mathematica Bohemica

We consider algebras determined by all normal identities of M V -algebras, i.e. algebras of many-valued logics. For such algebras, we present a representation based on a normalization of a sectionally involutioned lattice, i.e. a q -lattice, and another one based on a normalization of a lattice-ordered group.

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