More Results on Almost Noetherian Domains - Jabbar, Adil (Iraqi Journal of Science, 2025)
In this paper we prove some theorems, the first states: If R is an almostNoetherian domain, then the following statements are equivalent: ١- R is an almostDedekind domain.٢- A(B∩C)= AB∩AC, for all ideals A, B and C of R. ٣- (A+B)(A∩B)= AB, for allideals A and B of R and the second states: If R is an almost Noetherian domainwhich is not a field, then the following statements are equivalent: ١- R is a valuationdomain. ٢- The nonunits of R form a nonzero principal ideal of R. ٣- R is integrallyclosed and has exactly one nonzero proper prime ideal. In addition to the abovesome other results are proved.