Residuation in orthomodular lattices

• Autorzy: Ivan Chajda , Helmut Länger
• Języki publikacji: EN

Abstrakty

EN

We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one.

Słowa kluczowe

EN

residuated lattice; right residuated lattice; weak residuated lattice; orthomodular lattice; weak divisible; positive; double negation law

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 1-5

Daty

wydano

2017-04-25

otrzymano

2015-02-10

zaakceptowano

2015-09-15

online

2017-05-16

Twórcy

autor

Ivan Chajda

• ,,

autor

Helmut Länger

• ,,

Identyfikatory

DOI

10.1515/taa-2017-0001