Varieties generated by modular lattices of width four
Ralph S. Freese · Bulletin of the American Mathematical Society · 1972
The purpose of this paper is to announce some results of the author's thesis on modular width four lattices and their consequences particularly in the field of lattice varieties.Detailed proofs will appear elsewhere.A variety (equational class) of lattices is said to be finitely based if it is defined by a finite set of identities (see [2] for definitions).Let M™ be the variety generated by all modular lattices of width not exceeding n and length not exceeding m, where m and n are cardinals.It is easy to see that if n x and n 2 are infinite cardinals and m is any cardinal then MJ, 1 = M^2 and M * = M™ 2 .Consequently the symbol oo will be used in place of any infinite cardinal.R. Wille [8] asks for which m, n is MJJ 1 finitely based.If m FIGURE 1 AMS 1970 subject classifications.Primary 06A30, 08A15, 06A20; Secondary 08A30.