Sentence:  An <WSD>ideal</WSD> "A" of "L" is called complete if it contains all least upper bounds of its subsets that exist in "L". Bishop and Schreiner [80] studied conditions under which joins of <WSD>ideals</WSD> in the lattices of all <WSD>ideals</WSD> and of all complete <WSD>ideals</WSD> coincide. 
Meaning of the word marked with <WSD> tags:  A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).<ref>(Boolean prime ideal theorem#Prime ideal theorems)</ref>