Geodesic
Isomorphisms and automorphisms of matrix algebras over lattices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 1, pp. 195-204

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider the multiplicative groupoid of matrices with elements in a lattice with 0 and 1. Examples of such groupoids are the semigroup of binary relations and semigroups of minimax (fuzzy) relations. It is shown that every automorphism of a groupoid is the composition of an inner automorphism and the automorphism defined by an automorphism of the lattice. Despite the fact that, in general, the groupoid is not associative, it satisfies the UA-property: every multiplicative automorphism is an additive automorphism. Earlier, the realization of the UA-property has been considered mainly for associative rings and semirings. We describe the invertible matrices that define inner automorphisms. 
@article{FPM_2014_19_1_a9,
     author = {V. D. Shmatkov},
     title = {Isomorphisms and automorphisms of matrix algebras over lattices},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {195--204},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2014_19_1_a9/}
}
TY  - JOUR
AU  - V. D. Shmatkov
TI  - Isomorphisms and automorphisms of matrix algebras over lattices
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2014
SP  - 195
EP  - 204
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2014_19_1_a9/
LA  - ru
ID  - FPM_2014_19_1_a9
ER  - 
%0 Journal Article
%A V. D. Shmatkov
%T Isomorphisms and automorphisms of matrix algebras over lattices
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2014
%P 195-204
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2014_19_1_a9/
%G ru
%F FPM_2014_19_1_a9
V. D. Shmatkov. Isomorphisms and automorphisms of matrix algebras over lattices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 1, pp. 195-204. http://geodesic.mathdoc.fr/item/FPM_2014_19_1_a9/