关于具有多项式约束的I-环

On Lattice-Ordered Rings with Polynomial Constraints

中文摘要:

      

英文摘要:

      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 satifies a polynomial identity p(x)≥0 or f(x,y)≥0 (for suitable f(x,y)).