Geodesic
Integrally closed rings
Sbornik. Mathematics, Tome 43 (1982) no. 4, pp. 485-498 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper studies integrally closed rings. It is shown that a semiprime integrally closed Goldie ring is the direct product of a semisimple Artinian ring and a finite number of integrally closed invariant domains that are classically integrally closed in their (division) rings of fractions. It is shown also that an integrally closed ring has a classical ring of fractions and is classically integrally closed in it. Next, integrally closed Noetherian rings are considered. It is shown that an integrally closed Noetherian ring all of whose nonzero prime ideals are maximal is either a quasi-Frobenius ring or a hereditary invariant domain. Finally, those Noetherian rings all of whose factor rings are invariant are described, and the connection between integrally closed rings and distributive rings is examined. Bibliography: 13 titles. 
@article{SM_1982_43_4_a2,
     author = {A. A. Tuganbaev},
     title = {Integrally closed rings},
     journal = {Sbornik. Mathematics},
     pages = {485--498},
     year = {1982},
     volume = {43},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_43_4_a2/}
}
TY  - JOUR
AU  - A. A. Tuganbaev
TI  - Integrally closed rings
JO  - Sbornik. Mathematics
PY  - 1982
SP  - 485
EP  - 498
VL  - 43
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1982_43_4_a2/
LA  - en
ID  - SM_1982_43_4_a2
ER  - 
%0 Journal Article
%A A. A. Tuganbaev
%T Integrally closed rings
%J Sbornik. Mathematics
%D 1982
%P 485-498
%V 43
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1982_43_4_a2/
%G en
%F SM_1982_43_4_a2
A. A. Tuganbaev. Integrally closed rings. Sbornik. Mathematics, Tome 43 (1982) no. 4, pp. 485-498. http://geodesic.mathdoc.fr/item/SM_1982_43_4_a2/

[1] Feis K., Algebra: koltsa, moduli i kategorii, T. 1, Mir, M., 1977

[2] Feis K., Algebra: koltsa, moduli i kategorii, T. 2, Mir, M., 1979 | MR

[3] Tuganbaev A. A., “Kvaziin'ektivnye i maloin'ektivnye moduli”, Vestn. Mosk. un-ta, ser. matematika, mekhanika, 1977, no. 2, 61–64 | MR | Zbl

[4] Tuganbaev A. A., “Distributivnye nëterovy koltsa”, Vestn. Mosk. un-ta, ser. matematika, mekhanika, 1980, no. 2, 30–34 | MR | Zbl

[5] Small L. W., “Semihereditary rings”, Bull. Amer. Math. Soc., 73:5 (1967), 656–658 | DOI | MR | Zbl

[6] Lenagan T. N., “Bounded hereditary noetherian prime rings”, J. London Math. Soc., 6:2 (1973), 241–276 | DOI | MR

[7] Tuganbaev A. A., “Koltsa, nad kotorymi vse tsiklicheskie moduli maloin'ektivny”, Tr. seminara im. I. G. Petrovskogo, no. 6, MGU, 1981 | MR

[8] Zak A., “Some rings are hereditary”, Israel J. Math., 10:4 (1971), 442–450 | DOI | MR | Zbl

[9] Goodearl K. R., Ring theory. Nonsingular rings and modules, Marcel Dekker, New York, Basel, 1976 | MR | Zbl

[10] Stenstrom B., Rings of quotients, Springer-Verlag, Berlin e. a., 1975 | MR

[11] Brungs H. H., “Rings with a distributive lattice of right ideals”, J. Algebra, 40 (1976), 392–400 | DOI | MR | Zbl

[12] Osofsky B. L., “Noninjective cyclic modules”, Proc. Amer. Math. Soc., 19:6 (1968), 1383–1384 | DOI | MR | Zbl

[13] Kon P., Svobodnye koltsa i ikh svyazi, Mir, M., 1975 | MR