Sublogics of ring-like quantum logics

Rok, strany: 1998, 75 - 83

Motivated by the search for structures which generalize quantum logics and which are endowed with ring-like fundamental operations, the concepts of generalized Boolean quasirings (GBQRs) and Boolean quasirings (BQRs) were introduced in [D. Dorninger, H. Länger, M. Maczynski: The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215–232]. GBQRs are related to lattices with an involutory antiautomorphism and BQRs are in one-to-one correspondence with ortholattices. However, sublattices of the associated lattices do not correspond with subalgebras of the respective GBQRs and BQRs in general. In this paper subalgebras of various classes of GBQRs are characterized and their structure is investigated. In particular, a description of subalgebras of those GBQRs, which have a unique representation as bounded lattices with an involutory antiautomorphism, is given. Among these GBQRs there are the “orthomodular” GBQRs which turn out to be BQRs and are in one-to-one correspondence with orthomodular lattices.

ISO 690:

Dorninger, D. 1998. Sublogics of ring-like quantum logics. In Tatra Mountains Mathematical Publications, vol. 15, no.2, pp. 75-83. 1210-3195.

APA:

Dorninger, D. (1998). Sublogics of ring-like quantum logics. Tatra Mountains Mathematical Publications, 15(2), 75-83. 1210-3195.