×

zbMATH — the first resource for mathematics

Note on ideals of effect algebras. (English) Zbl 1166.03037
It is proved that the class of effect algebras in which every lattice ideal is an effect algebra ideal is the class of orthomodular lattices.

MSC:
03G12 Quantum logic
06C15 Complemented lattices, orthocomplemented lattices and posets
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Dvurečenskij, A.; Pulmannová, S., New trends in quantum structures, (2000), Kluwer Academic Publishers · Zbl 0987.81005
[2] Foulis, D.J.; Bennett, M.K., Effect algebras and unsharp quantum logics, Found. phys., 24, 1331-1352, (1994) · Zbl 1213.06004
[3] Chovanec, F.; Kôpka, F., D-lattices, Int. J. theor. phys., 34, 1297-1302, (1995) · Zbl 0840.03046
[4] Jenča, G., Notes on R1-ideals in partial abelian monoids, Algebra univ., 43, 307-319, (2000) · Zbl 1011.06017
[5] Chevalier, G.; Pulmannová, S., Some ideal lattices in partial abelian monoids and effect algebras, Order, 17, 75-92, (2000) · Zbl 0960.03053
[6] Ma, Z.H.; Wu, J.D.; Lu, S.J., Ideals and filters in pseudo-effect algebras, Int. J. theor. phys., 43, 1445-1451, (2004) · Zbl 1073.81010
[7] Hoo, C.S.; Murty, P.V.R., The ideals of a bounded commutative BCK-algebras, Math. jpn., 32, 723-733, (1987) · Zbl 0636.03060
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.