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More Results on Almost Noetherian Domains | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 50, Issue 0, 2009, Pages 53-58 | ||
| Author | ||
| Adil Kadir Jabbar | ||
| Abstract | ||
| 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 all 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 of R. 3- R is integrally closed and has exactly one nonzero proper prime ideal. In addition to the above some other results are proved. | ||
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