Geodesic
A note on the FIP property for extensions of commutative rings
Filomat, Tome 33 (2019) no. 19, p. 6213

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DOI

A ring extension R ⊂ S is said to be FIP if it has only finitely many intermediate rings between R and S. The main purpose of this paper is to characterize the FIP property for a ring extension, where R is not (necessarily) an integral domain and S may not be an integral domain. Precisely, we establish a generalization of the classical Primitive Element Theorem for an arbitrary ring extension. Also, various sufficient and necessary conditions are given for a ring extension to have or not to have FIP, where S = R[α] with α a nilpotent element of S
DOI : 10.2298/FIL1919213B
Classification : 13B02, 13A15, 13B21, 13B25, 13E05, 13E10
Keywords: FIP property, ring extension, intermediate ring, minimal ring extension, integral, nilpotent element 
Mabrouk Ben Nasr; Nabil Zeidi. A note on the FIP property for extensions of commutative rings. Filomat, Tome 33 (2019) no. 19, p. 6213 . doi: 10.2298/FIL1919213B
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     title = {A note on the {FIP} property for extensions of commutative rings},
     journal = {Filomat},
     pages = {6213 },
     year = {2019},
     volume = {33},
     number = {19},
     doi = {10.2298/FIL1919213B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL1919213B/}
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