A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation.
@article{bwmeta1.element.doi-10_1515_math-2016-0030,
author = {Qimei Xiao and Wenjun Liu},
title = {On derivations of quantales},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {338-346},
zbl = {1353.06012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0030}
}
Qimei Xiao; Wenjun Liu. On derivations of quantales. Open Mathematics, Tome 14 (2016) pp. 338-346. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0030/