On Grätzer's problem (Q1267369)

Grätzer's Problem 1.4 consists in finding conditions under which a lattice \(L\) is determined up to isomorphism by \(\text{Sub}(L)\). The main result of the present paper gives a sufficient condition for a lattice \(L\) under which \(L\) is determined by \(\text{Sub}(L)\) up to an isomorphism or a dual isomorphism. This extends some previous results of the author [Hanoi Univ. J. Sci. 4, 8-12 (1993); Vietnam J. Math. 24, 75-82 (1996); Vietnam Natl. Univ. J. Sci. 3, 6-9 (1995)].