Page 288 - Leech, Jonathan E. 2020. Noncommutative Lattices: Skew Lattices, Skew Boolean Algebras and Beyond. Koper: University of Primorska Press
P. 288
Jonathan E. Leech
NONCOMMUTATIVE LATTICES:
Skew Lattices, Skew Boolean Algebras and Beyond
The extended study of non-commutative lattices was be-
gun in 1949 by Ernst Pascual Jordan, a theoretical and
mathematical physicist and co-worker of Max Born and
Werner Karl Heisenberg. Jordan introduced noncommu-
tative lattices as algebraic structures potentially suita-
ble to encompass the logic of the quantum world. The
modern theory of noncommutative lattices began forty
years later with Jonathan Leech’s 1989 paper “Skew lat-
192329313741tices in rings.” Recently, noncommutative generalizations
of lattices and related structures have seen an upsurge in
interest, with new ideas and applications emerging, from
3127131137139149151157quasilattices to skew Heyting algebras. Much of this ac-
tivity is derived in some way from the initiation of Jona-
233239241251257263269271277281283293307491499503509521bt5ho2ao3nk5L4c1oe5en4csh7is5’ts5s7p5or6fo3gs5er6av9me5n7oc1fh5r7ae7ps5te8ear7rs5c,9h m3i5na9i9tnh6ly0is1c6ao0rve7ea6r.1in3T6gh17esk6p1e9rwe6s3lea1nt6t-41643647653659
tices, quasilattices and paralattices, skew lattices of idem-
potents in rings and skew Boolean algebras. As such, it is
the first research monograph covering major results due
to this renewed study of noncommutative lattices. It will
serve as a valuable graduate textbook on the subject, as
well as a handy reference to researchers of noncommuta-
tive algebras.
Založba Univerze na Primorskem
Titov trg 4, SI-6000 Koper
www.hippocampus.si
zalozba@upr. si
NONCOMMUTATIVE LATTICES:
Skew Lattices, Skew Boolean Algebras and Beyond
The extended study of non-commutative lattices was be-
gun in 1949 by Ernst Pascual Jordan, a theoretical and
mathematical physicist and co-worker of Max Born and
Werner Karl Heisenberg. Jordan introduced noncommu-
tative lattices as algebraic structures potentially suita-
ble to encompass the logic of the quantum world. The
modern theory of noncommutative lattices began forty
years later with Jonathan Leech’s 1989 paper “Skew lat-
192329313741tices in rings.” Recently, noncommutative generalizations
of lattices and related structures have seen an upsurge in
interest, with new ideas and applications emerging, from
3127131137139149151157quasilattices to skew Heyting algebras. Much of this ac-
tivity is derived in some way from the initiation of Jona-
233239241251257263269271277281283293307491499503509521bt5ho2ao3nk5L4c1oe5en4csh7is5’ts5s7p5or6fo3gs5er6av9me5n7oc1fh5r7ae7ps5te8ear7rs5c,9h m3i5na9i9tnh6ly0is1c6ao0rve7ea6r.1in3T6gh17esk6p1e9rwe6s3lea1nt6t-41643647653659
tices, quasilattices and paralattices, skew lattices of idem-
potents in rings and skew Boolean algebras. As such, it is
the first research monograph covering major results due
to this renewed study of noncommutative lattices. It will
serve as a valuable graduate textbook on the subject, as
well as a handy reference to researchers of noncommuta-
tive algebras.
Založba Univerze na Primorskem
Titov trg 4, SI-6000 Koper
www.hippocampus.si
zalozba@upr. si
