A note on symmetric differences of orthomodular lattices
Commun. Korean Math. Soc. 2003 Vol. 18, No. 2, 207-214 Printed June 1, 2003
Eunsoon Park, Mi Mi Kim, Jin Young Chung Soongsil University, Kansas State University
Abstract : There exist two distinct symmetric differences in a non Boolean orthomodular lattice. Let $L$ be an orthomodular lattice. Then $L$ is a Boolean algebra if and only if one symmetric difference is equal to the other. An orthomodular lattice $L$ is Boolean if and only if one of two symmetric differences of $L$ is associative.