Given a complete and atomic Boolean algebra B, there exists a family taugamma of triangular norms on B such that, under the partial ordering of triangular norms, taugamma is a Boolean algebra isomorphic to B, where gamma is the set of all atoms in B. In other words, as we have shown in this note, every complete and atomic Boolean algebra can be represented by its own triangular norms. What we have not shown in this paper is our belief that taugamma is not unique for B and that, for such a representation, B needs neither to be complete, nor to be atomic.
@article{urn:eudml:doc:39097,
title = {Representation of a Boolean algebra by its triangular norms.},
journal = {Mathware and Soft Computing},
volume = {4},
year = {1997},
pages = {63-68},
zbl = {0873.06009},
mrnumber = {MR1463109},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39097}
}
Ray, Suryansu. Representation of a Boolean algebra by its triangular norms.. Mathware and Soft Computing, Tome 4 (1997) pp. 63-68. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39097/