Geodesic
When is $\mathbb{Z}[\alpha]$ seminormal or $t$-closed?
Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 1, pp. 189-217.

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Sia a un intero algebrico con il polinomio minimale $f(X)$. Si danno condizioni necessarie e sufficienti affinché l'anello $\mathbb{Z}[\alpha]$ sia seminormale o $t$-chiuso per mezzo di $f(X)$. Come applicazione, in particolare, si ottiene che se $f(X)=X^{3}+aX+b$, $a$, $b \in \mathbb{Z}$ le condizioni sono espresse mediante il discriminante de $f(X)$. 
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Picavet-L'Hermitte, Martine. When is $\mathbb{Z}[\alpha]$ seminormal or $t$-closed?. Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 1, pp. 189-217. http://geodesic.mathdoc.fr/item/BUMI_1999_8_2B_1_a8/

[1] T. Albu , On a paper of Uchida concerning simple finite extensions of Dedekind domains, Osaka J. Math., 16 (1979), 65-69. | fulltext mini-dml | MR | Zbl

[2] D. F. Anderson - D. E. Dobbs - J. A. Huckaba , On seminormal overrings, Comm. Algebra, 10 (1982), 1421-1448. | MR | Zbl

[3] D. E. Dobbs - M. Fontana , Seminormal rings generated by algebraic integers, Matematika, 34 (1987), 141-154. | MR | Zbl

[4] D. Ferrand - J. P. Olivier , Homomorphismes minimaux d'anneaux, J. Algebra, 16 (1970), 461-471. | MR | Zbl

[5] G. Maury , La condition «intégralement clos» dans quelques structures algébriques, Ann. Sci. Ecole Norm. Sup., 78 (1961), 31-100. | fulltext mini-dml | MR | Zbl

[6] G. Picavet - M. Picavet-L'Hermitte , Morphismes $t$-clos, Comm. Algebra, 21 (1993), 179-219. | MR | Zbl

[7] G. Picavet - M. Picavet-L'Hermitte , Anneaux $t$-clos, Comm. Algebra, 23 (1995), 2643-2677. | MR | Zbl

[8] M. Picavet-L'Hermitte , Decomposition of order morphisms into minimal morphisms, Math. J. Toyama Univ., 19 (1996), 17-45. | MR | Zbl

[9] P. Samuel , Théorie Algébrique des Nombres (Hermann, Paris) 1967. | MR | Zbl

[10] R. G. Swan , On seminormality, J. Algebra, 67 (1980), 210-229. | MR | Zbl

[11] H. Tanimoto , Normality, seminormality and quasinormality of $\mathbb{Z}[\sqrt[n]{m}]$, Hiroshima Math. J., 17 (1987), 29-40. | fulltext mini-dml | MR | Zbl

[12] K. Uchida , When is $\mathbb{Z}[\alpha]$ the ring of the integers?, Osaka J. Math., 14 (1977), 155-157. | fulltext mini-dml | MR | Zbl