Geodesic
Arithmetical rings and Krull dimension
Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 126-132

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Let $A$ be a commutative arithmetical ring. It is proved that the ring $A$ has Krull dimension if and only if every factor ring of $A$ is finite-dimensional and does not have idempotent proper essential ideals.
Keywords: arithmetical ring, Krull dimension, idempotent ideal. 
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     author = {A. A. Tuganbaev},
     title = {Arithmetical rings and {Krull} dimension},
     journal = {Diskretnaya Matematika},
     pages = {126--132},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2017_29_3_a8/}
}
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A. A. Tuganbaev. Arithmetical rings and Krull dimension. Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 126-132. http://geodesic.mathdoc.fr/item/DM_2017_29_3_a8/