摘要
一、引言设R是一个l-环(Lattice—ordered ring),F是一个可换的有单位元的全序整环.R称为F上的l-代数,如果R是F上的无扭代数和F上的f-模.F上的l-代数R称为F上的f-代数,若R是一个f-环。令T={r∈R:u∧v=0(?)|r|u∧v=u|r|∧v=0,(?)u,v∈R},T中的正元素称为R的f-元.
In this paper, it is shown that an l-prime lattice-ordered ring in which the square of every element is positive must be a domain provided it has non-zero f-elements and be an l-domain provided it has a left (right) identity ele-ment or a central idempotent element .More generally,the same conclusion follows if the condition a2≥0 is replaced by p(a)≥0 or f(a,b)≥0 for suitable polyno-mials p(x) and f(x, y) . It is also shown that an l-algebra is an f-algebra provided it is archimedean, contains an f-element e>0 with r1(e) = 0, and sat-ifies a polynomial identity p(x)≥0 or f(x, y)≥0 (for suitable f(x, y)).
