Publication details

Blocks in Pairwise Summable Generalized Effect Algebras



Year of publication 2014
Type Article in Periodical
Magazine / Source Reports on Mathematical Physics
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords (generalized) effect algebra; MV-effect algebra; summability block; compatibility block; linear operators in Hilbert spaces
Description We study so called pairwise summable generalized effect algebras and show some conditions under which they are generalized MV-effect algebras. Moreover, we give a necessary and sufficient condition for finite antichains of elements in pairwise summable generalized effect algebras under which they are sets of atoms of sub-generalized effect algebras, which are generalized MV-effect algebras in their own right. Simultaneously, we give counterexamples which show properties of those antichains which are not necessary or sufficient to be atoms of such generalized MV-effect algebras.
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