an:05242742
Zbl 1135.06004
Ischi, Boris
Weak tensor products of complete atomistic lattices
EN
Algebra Univers. 57, No. 2, 239-258 (2007).
00212979
2007
j
06B23 03G12 06C15 81P10
complete atomistic lattice; tensor product; quantum logic
The author introduces the notion of the set of weak tensor products of complete atomistic lattices. He shows that the bottom element of this set coincides with the separated product of Aerts for orthocomplemented lattices and that a slight modification gives the box product of \textit{G. Gr??tzer} and \textit{F. Wehrung} [Algebra Univers. 41, No. 2, 87--114 (1999; Zbl 0965.06008)].
On the other hand, the top element of this set for a pair of lattices coincides with tensor products of Chu, \textit{Z. Shmuely} [Pac. J. Math. 54, No. 2, 209--225 (1974; Zbl 0275.06003)] and \textit{G. A. Fraser} [Trans. Am. Math. Soc. 217, 183--194 (1976; Zbl 0355.06013)]. The automorphisms of weak tensor products are characterized provided some additional assumptions are fulfilled.
Josef Tkadlec (Praha)
Zbl 0965.06008; Zbl 0275.06003; Zbl 0355.06013