Geodesic
Cancellation ideals of a ring extension
Algebra and discrete mathematics, Tome 32 (2021) no. 1, pp. 138-146

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We study properties of cancellation ideals of ring extensions. Let $R \subseteq S$ be a ring extension. A nonzero $S$-regular ideal $I$ of $R$ is called a (quasi)-cancellation ideal of the ring extension $R \subseteq S$ if whenever $IB = IC$ for two $S$-regular (finitely generated) $R$-submodules $B$ and $C$ of $S$, then $B =C$. We show that a finitely generated ideal $I$ is a cancellation ideal of the ring extension $R\subseteq S$ if and only if $I$ is $S$-invertible.
Keywords: ring extension, cancellation ideal, pullback diagram. 
@article{ADM_2021_32_1_a8,
     author = {S. Tchamna},
     title = {Cancellation ideals of a ring extension},
     journal = {Algebra and discrete mathematics},
     pages = {138--146},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a8/}
}
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S. Tchamna. Cancellation ideals of a ring extension. Algebra and discrete mathematics, Tome 32 (2021) no. 1, pp. 138-146. http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a8/