@article{Ayache_2019, title={Maximal non-decreasing subring of its quotient field}, volume={7}, url={https://gjom.org/index.php/gjom/article/view/3}, abstractNote={<p>An integral domain <em>R</em> is called maximal non-going down subring of its quotient field, if <em>R</em> is not going down, and every proper overring of <em>R</em> is going down. We do prove that R is a maximal non-going down subring of its quotient field if and only if <em>R</em> is a quasi-local domain with maximal ideal m and its integral closure <em>R</em> is a semi-local Prufer domain with two maximal ideals <em>M</em>, <em>N</em> such that <em>M</em> intersect <em>N</em> = <em>m</em>, the extension <em>R</em> is not going down, and <em>R</em> is the unique quasi-local subring of <em>R</em>.</p>}, number={3}, journal={Gulf Journal of Mathematics}, author={Ayache, Ahmed}, year={2019}, month={Sep.} }