Geodesic
The canonical module and anti-invariant elements
Izvestiya. Mathematics , Tome 11 (1977) no. 6, pp. 1151-1174.

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Let $S$ be a ring having canonical module; let $\mathfrak G$ be a finite group of automorphisms of this ring, and let $R$ be the subring of elements of $S$ invariant with respect to the action of $\mathfrak G$. We study the problem of existence and characterization of the canonical module of the ring $R$. In particular we apply our results to the problem of descent of the Gorenstein property of a ring. Bibliography: 19 titles. 
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     title = {The canonical module and anti-invariant elements},
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S. S. Strogalov. The canonical module and anti-invariant elements. Izvestiya. Mathematics , Tome 11 (1977) no. 6, pp. 1151-1174. http://geodesic.mathdoc.fr/item/IM2_1977_11_6_a1/

[1] Serr Zh.-P., “Lokalnaya algebra i teoriya kratnostei”, Matematika, 7:5 (1963), 3–93

[2] Bass H., “On the ubiquity Gorenstein rings”, Math. Z., 82:1 (1963), 8–23 | DOI | MR

[3] Avramov L. L., Strogalov S. S., Todorov A. N., “O modulyakh Gorenshteina”, Uspekhi matem. nauk, 27:4 (1972), 199–200 | MR | Zbl

[4] Fossum R., Griffith P., Reiten I., “Trivial extensions of abelian categories”, Lect. Notes in Math., 466, 1975 | MR

[5] Strogalov S. S., “Spusk kanonicheskogo modulya dlya kolets invariantov”, Uspekhi matem. nauk, 30:6 (1975), 185–186 | MR | Zbl

[6] Strogalov S. S., Tretii Vsesoyuznyi algebraicheskii simpozium (koltsa, algebry, moduli), tezisy dokladov, Tartu, Kyaeriku, 1976 | Zbl

[7] Kartan A., Eilenberg S., Gomologicheskaya algebra, IL, M., 1960

[8] Gulliksen T. H., “A proof of existence of minimal $R$-algebra resolution”, Acta Math., 120 (1968), 53–58 | DOI | MR | Zbl

[9] Auslander M., Buchsbaum D. A., “Codimension and multiplicity”, Ann. Math., 68 (1958), 625–657 | DOI | MR | Zbl

[10] Tate J., “Homology of noetherian rings and of local rings”, Illinois J. of Math., 1:1 (1957), 14–27 | MR | Zbl

[11] Assmus E. F., “On the homology of local rings”, Illinois J. of Math., 3:2 (1959), 187–199 | MR | Zbl

[12] Burbaki N., Gruppy i algebry Li, Mir, M., 1972 | MR | Zbl

[13] Eagon J. A., Hochster M., “Cohen–Macaulay rings, invariant theory and the generic perfection determinantal loci”, Amer. J. Math., 93:4 (1971), 1020–1058 | DOI | MR | Zbl

[14] Burbaki N., Kommutativnaya algebra, Mir, M., 1971 | MR

[15] Leng S., Algebra, Mir, M., 1968

[16] Khinich V. A., “O gorenshteinovosti koltsa invariantov koltsa Gorenshteina”, Izv. AN SSSR. Ser. matem., 40 (1976), 50–56 | Zbl

[17] Watanabe K., “Certain invariant subrings are Gorenstein”, Osaka J. Math., II (1974), 1–8 | MR

[18] Lambek I., Koltsa i moduli, Mir, M., 1971 | MR | Zbl

[19] Strogalov S. S., “O ploskikh morfizmakh”, Uspekhi matem. nauk, 31:4 (1976), 277–278 | MR | Zbl