ACTA issues

Baer lattices

D. D. Anderson, C. Jayaram, P. A. Phiri

Acta Sci. Math. (Szeged) 59:1-2(1994), 61-74

Abstract. Let $L$ be a reduced, compactly generated multiplicative lattice in which 1 is compact and every finite product of compact elements is compact. In this setting we study quasiregular lattices (for every compact element $x\in L$, there exists a compact element $y\in L$ with $(0:(0:x))=(0:y))$, regular lattices (every compact element is complemented), and Baer lattices (for every compact element $x$, $(0:x)\vee(0:(0:x))=1)$.

AMS Subject Classification (1991): 06F10, 06E99

Keyword(s): quasiregular lattices, Baer lattices, multiplicative lattices, compact elements

Received October 26, 1992 (Registered under 5572/2009.)