A Note on Janowitz's Hulls of Generalized Orthomodular Lattices
Commun. Korean Math. Soc. 2000 Vol. 15, No. 3, 511-519
Eunsoon Park, Jin Young Chung Soongsil University, Soongsil University
Abstract : If $G$ is a strict generalized orthomodular lattice and $H = \{ I |I = [0, x],$ $ x \in G\}$, then $H$ is a prime ideal of the Janowitz's hull $J(G)$ of $G$. If $f$ is the Janowitz's embedding, then the set of all commutators of $f(G)$ equals the set of all commutators of the Janowitz's hull $J(G)$ of $G$. Let $L$ be an OML. Then $L\simeq J(G)$ for a strict GOML $G$ if and only if there exists a proper nonprincipal prime ideal $G$ in $L$.
