@@ -42,7 +42,7 @@ Birkhoff and Lipson (1968) have defined a heterogeneous algebra as a system A=[
1. Σ={S~i~} is a family of non-void sets S~i~ of different types of elements, each called a *phylum* of the algebra A. The *phyla* S~i~ are indexed by some set I; i.e. S~i~∈Σ for i∈I (or are called by appropriate names).
2. F={f~α~} is a set of finitary operations, where each f~α~ is a mapping f~α~:S~i(1,α)~×S~i(2,α)~×⋯ ×S~i(n(α),α)~→S~r(α)~
for some non-negative interger n(α), function i~α~:k→i(k,α) from {1,2,⋯,n(α)} to I, and r(α)∈I. The operations f~α~ are indexed by some set Ω; i.e. f~α~∈F for α∈Ω (or are called by appropriate names).
for some non-negative integer n(α), function i~α~:k→i(k,α) from {1,2,⋯,n(α)} to I, and r(α)∈I. The operations f~α~ are indexed by some set Ω; i.e. f~α~∈F for α∈Ω (or are called by appropriate names).
Thus each operation f~α~ assigns to each n(α)-tuple (x~1~,⋯,x~n~(α) ), where x~j~∈S_(i(j,α)), some value f~α~ (x~1~,⋯,x~n(α)~ ) in S~r(α)~. The operation f_α is said to be n(α)-ary: unary when n(α)=1, binary when n(α)=2, ternary when n(α)=3, etc. When n(α)=0, it selects a fixed element (distinguished constant) of S_(r(α)).
