International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 301-309

Idempotent and compact matrices on linear lattices: a survey of some lattice results and related solutions of finite relational equations

Fortunata Liguori, Giulia Martini, and Salvatore Sessa

Università di Napoli, Facoltà di Architettura, Istituto Matematico, Via Monteoliveto 3, Napoli 80134, Italy

Received 4 February 1991

Copyright © 1993 Fortunata Liguori et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


After a survey of some known lattice results, we determine the greatest idempotent (resp. compact) solution, when it exists, of a finite square rational equation assigned over a linear lattice. Similar considerations are presented for composite relational equations.