More results on almost noetherian domains

Abstract EN

In this paper we prove some theorems, the first states : If R is an almost Noetherian domain, then the following statements are equivalent : 1- R is an almost Dedekind domain.

2- A (B ∩ C) = AB ∩ AC, for all ideals A, B and C of R 3- (A + B) (A ∩ B) = AB, for al ideals A and B of R and the second states : if R is an almost Noetherian domain which is not a field, then the following statements are equivalent 1- R is a valuation domain.

2- The nonunits of R form a nonzero principal ideal 3- R is integrally closed and has exactly one nonzero proper prime ideal.

In addition to the above some other results are proved.