Poproduct of lattices
Zuzana Ladzianska · Czech digital mathematics library · 1982
POPRODUCT OF LATTICES ZUZANA LADZIANSKAThe poproduct was introduced for the class of distributive lattices by R. Balbes and A. Horn [2] under the name order sum.The notion of the .^-poproductfor an arbitrary equational class % of lattices was defined in [11].The .vlf-poproduct is a generalization of the ^T-free product and the ordinal sum of lattices.M. Hof t [8] defined the order sum for the class of partially ordered algebras and showed that the order sum exists in each quasi-equational class.If 3if is an equational class of lattices, then the ^f-poproduct always exists and coincides with the order sum.The 3if-poproduct was considered by T. G. Kucera and B. Sands [10] under the name Ф,.,4The present paper consists of five parts, in which various problems concerning a poproduct are considered.