Geodesic
On the structure of locally compact biregular rings
Sbornik. Mathematics, Tome 33 (1977) no. 4, pp. 573-577 
L. A. Skornyakov. On the structure of locally compact biregular rings. Sbornik. Mathematics, Tome 33 (1977) no. 4, pp. 573-577. http://geodesic.mathdoc.fr/item/SM_1977_33_4_a6/
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     title = {On~the structure of locally compact biregular rings},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is established that the results of a previous paper by the author (Mat. Sb. (N.S.), 62(104), 1963, 3–13) are valid only if their statements are modified and conditionally simple rings are considered instead of simple ones. Here a conditionally simple ring is a topological ring which has a discrete maximal ideal. There is given an example of a nondiscrete conditionally simple locally compact biregular ring with identity in which the above discrete maximal ideal is not a direct summand. Bibliography: 13 titles.

[1] V. I. Arnautov, V. N. Vizitiu, “Prodolzhenie lokalno ogranichennoi topologii polya na ego algebraicheskoe rasshirenie”, Izv. AN Mold. SSR, seriya fiz.-tekh. i matem. nauk, 1974, no. 2, 29–43 | MR | Zbl

[2] N. Burbaki, Obschaya topologiya, osnovnye struktury, Fizmatgiz, Moskva, 1958

[3] Dzh. Dauns, K. Gofman, “Predstavlenie biregulyarnykh kolets puchkami”, Matematika, 12:4 (1968), 3–24

[4] L. S. Pontryagin, Nepreryvnye gruppy, izd-vo «Nauka», Moskva, 1973 | MR

[5] L. Skornyakov, Dedekindovy struktury s dopolneniyami i regulyarnye koltsa, Fizmatgiz, Moskva, 1961

[6] L. A. Skornyakov, “Lokalno bikompaktnye biregulyarnye koltsa”, Matem. sb., 62 (104) (1963), 3–13 | Zbl

[7] L. A. Skornyakov, “Lokalno bikompaktnye biregulyarnye koltsa (dobavlenie)”, Matem. sb., 69 (111) (1966), 663 | Zbl

[8] L. A. Skornyakov, “Einfache lokal bikompakte Ringe”, Math. Z., 87 (1965), 241–251 | DOI | MR | Zbl

[9] M. I. Ursul, “Lokalno nasledstvenno lineino kompaktnye biregulyarnye koltsa bez nilpotentnykh elementov. Algebry i moduli”, Matem. issledovaniya, no. 48, Kishinev, 1978

[10] B. M. Shain, “$O$-koltsa i $\bar{L}A$-koltsa”, Izvestiya VUZov, matematika, 1966, no. 2, 111–122

[11] I. Kaplansky, “Topological rings”, Amer. J. Math., 69 (1947), 153–183 | DOI | MR | Zbl

[12] I. Kaplansky, “Topological rings, I”, Amer. J. Math., 70 (1948), 447–459 | DOI | MR | Zbl

[13] I. Kaplansky, “Topological rings, II”, Amer. J. Math., 73 (1951), 20–24 | DOI | MR | Zbl