caa a22 4500 605523266 CHVBK 20210128100748.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10958-015-2614-z doi (NATIONALLICENCE)springer-10.1007/s10958-015-2614-z Shmatkov V. Ryazan State Radio Engineering University, Ryazan, Russia aut Isomorphisms and Automorphisms of Matrix Algebras Over Lattices [Elektronische Daten] [V. Shmatkov] 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. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 211/3(2015-12-01), 434-440 1072-3374 211:3<434 2015 211 10958 https://doi.org/10.1007/s10958-015-2614-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2614-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Shmatkov V. Ryazan State Radio Engineering University, Ryazan, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 211/3(2015-12-01), 434-440 1072-3374 211:3<434 2015 211 10958