TY - JOUR
ID - 31184
TI - THE INTERNAL IDEAL LATTICE IN THE
TOPOS OF M-SETS
JO - Journal of Sciences, Islamic Republic of Iran
JA - JSCIENCES
LA - en
SN - 1016-1104
Y1 - 1994
PY - 1994
VL - 5
IS - 2
SP -
EP -
DO -
N2 - We believe that the study of the notions of universal algebra modelled in an
arbitarry topos rather than in the category of sets provides a deeper
understanding of the real features of the algebraic notions. [2], [3], [4], [S], [6],
[7], [13], [14] are some examples of this approach. The lattice Id(L) of ideals of
a lattice L (in the category of sets) is an important ingredient of the category of
lattices. In this paper, we construct the (internal) ideal lattice T(A) of a lattice
A in the topos of M-sets for a monoid M. The process of the construction of
Y(A) is so that it can also be done in any arbitrary topos whose ingredients are
known. Finally, we consider the lattice structure of T(A) for some special kind
of lattices A in the topos of M-sets and show, among other things, that if A is
an internally complete M-Boolean algebra then Y(A) is an M-Stone lattice
UR - https://jsciences.ut.ac.ir/article_31184.html
L1 - https://jsciences.ut.ac.ir/article_31184_677e95291946119127dfdad1089697ad.pdf
ER -