Geodesic
On some properties of extensions of commutative unital rings
Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 4, pp. 7-10

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We find necessary and sufficient conditions for the ring $R[\alpha]$ to be either a field or a domain whenever $R$ is a commutative ring with 1 and $\alpha$ is an algebraic element over $R$. This continues the studies started by Nachev (Compt. Rend. Acad. Bulg. Sci., 2004) and (Commun. Alg., 2005) as well as their generalization due to Mihovski (Compt. Rend. Acad. Bulg. Sci., 2005). 
@article{VMJ_2009_11_4_a1,
     author = {P. V. Danchev},
     title = {On some properties of extensions of commutative unital rings},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {7--10},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2009_11_4_a1/}
}
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P. V. Danchev. On some properties of extensions of commutative unital rings. Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 4, pp. 7-10. http://geodesic.mathdoc.fr/item/VMJ_2009_11_4_a1/