VALUES AND MINIMAL SPECTRUM OF AN ALGEBRAIC LATTICE
George Georgescu, Miroslav Ploščica · Czech digital mathematics library · 2002
Algebraic lattices constitute an appropriate setting for generalizing the results existing in particular structures, as l-groups, MV-algebras, etc.. In this paper we study the very large elements and the very large radical of an algebraic lattice. We also define and characterize compactly generated algebraic lattices. Our results are generalizations of some theorems proved for l-groups in (Bigard, A.—Conrad, P.—Wolfenstein, S.: Compactly generated lattice-ordered groups ,M ath. Z.107 (1968), 201-211), (Conrad, P.—Martinez, J.: Very large subgroups of lattice-ordered groups, Comm. Algebra 18 (1990), 2063-2098), (Conrad, P.—Martinez, J.: Complemented lattice-ordered groups, Indag. Math. (N.S.) 1 (1990), 281-298) and for MV-algebras in (Di Nola, A.—Georgescu, G.— Sessa, S.: Closed ideals of MV-algebras. In: Advances in Contemporary Logic and Computer Science (W. A. Carnielli, I. M. L. D'Ottaviano eds.). Contemp. Math. 235, Amer. Math. Soc., Providence, RI, 1999, pp. 99-111).