On Lattice-Ordered Rings with Polynomial Constraints
Received:August 07, 1989  
Key Word:   
Fund ProjectL:
Author NameAffiliation
Ma Jingjing 北京人才交流中心 
Hits: 1269
Download times: 583
Abstract:
      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)).
Citation:
DOI:10.3770/j.issn:1000-341X.1991.03.002
View Full Text  View/Add Comment  Download reader