More Results on Almost Noetherian Domains
DOI:
https://doi.org/10.24996/ijs.2009.50.Appendix.%25gKeywords:
Almost, DomainsAbstract
In this paper we prove some theorems, the first states: If R is an almost
Noetherian domain, then the following statements are equivalent: ١- R is an almost
Dedekind domain.
٢- A(B∩C)= AB∩AC, for all ideals A, B and C of R. ٣- (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: ١- R is a valuation
domain. ٢- The nonunits of R form a nonzero principal ideal of R. ٣- 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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Published
2025-01-14
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Section
Mathematics
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Copyright (c) 2025 Iraqi Journal of Science
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
[1]
A. . . Jabbar, “More Results on Almost Noetherian Domains”, Iraqi Journal of Science, vol. 50, no. Appendix, pp. 53–58, Jan. 2025, doi: 10.24996/ijs.2009.50.Appendix.%g.
