Abstract. We characterize varieties of algebras for which the congruence kernel is determined by any congruence class.

AMS Subject Classification (1991): 08B05, 08A30

Keyword(s): Regularity, weak regularity, local regularity, Mal'cev condition

Received February 26, 1998 and in final form June 15, 1998. (Registered under 3297/2009.)