TY - JOUR
ID - 104001
TI - Idempotent 2x2 matrices over linearly ordered abelian groups
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Laan, Valdis
AU - Kutti, Marilyn
AD - Institute of Mathematics and Statistics, University of Tartu, Tartu, Estonia
Y1 - 2023
PY - 2023
VL -
IS -
SP -
EP -
KW - Matrix
KW - linearly ordered abelian group
KW - $0$-primitive idempotent
KW - full idempotent
KW - regular semigroup
DO - 10.48308/cgasa.2023.232266.1412
N2 - In this paper we study multiplicative semigroups of $2\times 2$ matrices over a linearly ordered abelian group with an externally added bottom element. The multiplication of such a semigroup is defined by replacing addition and multiplication by join and addition in the usual formula defining matrix multiplication. We show that there are four types of idempotents in this semigroup and we determine which of them are $0$-primitive. We also prove that the poset of idempotents with respect to the natural order is a lattice. It turns out that this matrix semigroup is inverse or orthodox if and only if the abelian group is trivial.
UR - https://cgasa.sbu.ac.ir/article_104001.html
L1 - https://cgasa.sbu.ac.ir/article_104001_6f3bc63a18e0e31a141fe9046f5f5e2e.pdf
ER -