Geodesic
On the structural theory and theory of radicals
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2019), pp. 74-94.

Voir la notice de l'article provenant de la source Math-Net.Ru

This is an overview published in Russian in the book devoted to Academician V. A. Andrunakievich Academicianul Vladimir Andrunachievichi: Bibliografie, Institutul de Matematică şi Informatică, Chişinău, 2009. 
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Yu. M. Ryabukhin. On the structural theory and theory of radicals. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2019), pp. 74-94. https://geodesic-test.mathdoc.fr/item/BASM_2019_3_a7/

[1] V. A. Andrunakievich, Semi-radical rings, Thesis of the Candidate of Phys.-Math. sciences, Moscow State University, M., 1946 (in Russian) | MR

[2] V. A. Andrunakievich, “Semi-radical and radical rings”, Uspekhi Mat. Nauk, 2:1 (1947) (in Russian) | MR

[3] V. A. Andrunakievich, “Semi-radical and radical rings”, (Doklady) Acad. Sci. URSS, 55:1 (1947), 3–5 (in Russian) | MR | Zbl

[4] V. A. Andrunakievich, “Semi-radical rings”, Izv. Akad. Nauk SSSR, Ser. Mat., 12:2 (1948), 129–178 (in Russian) | MR | Zbl

[5] V. A. Andrunakievich, “On the determination of the radical of a ring”, Izv. Akad. Nauk SSSR, Ser. Mat., 16:2 (1952), 217–224 (in Russian) | MR | Zbl

[6] V. A. Andrunakievich, Linear equations in infinite-dimensional spaces, Uch. Notes of Chisinau Univesity, 5, 1952 (in Russian)

[7] V. A. Andrunakievich, “The radical in generalized Q-sets”, Izv. Akad. Nauk SSSR, Ser. Mat., 18:5 (1954), 419–426 (in Russian) | MR | Zbl

[8] V. A. Andrunakievich, “Rings with the minimality condition for ideals”, Dokl. Akad. Nauk SSSR, 98:3 (1954), 329–332 (in Russian) | MR | Zbl

[9] V. A. Andrunakievich, “Rings with minimal two-sided ideals”, Dokl. Akad. Nauk SSSR, 100:3 (1955), 405–408 (in Russian) | MR | Zbl

[10] V. A. Andrunakievich, “Rings with the minimality condition for two-sided ideals”, Uspekhi Mat. Nauk, 10:2 (1955) (in Russian) | MR | Zbl

[11] V. A. Andrunakievich, “Rings with annihilator condition”, Izv. Akad. Nauk SSSR, Ser. Mat., 20:4 (1956), 547–568 (in Russian) | MR | Zbl

[12] V. A. Andrunakievich, “Biregular rings”, Mat. Sb., 39:4 (1956), 447–464 (in Russian) | MR | Zbl

[13] V. A. Andrunakievich, “On some classes of associative rings”, Uspekhi Mat. Nauk, 11:4 (1956) (in Russian) | MR | Zbl

[14] V. A. Andrunakievich, “To the theory of radicals of associative rings”, Dokl. Akad. Nauk SSSR, 113:3 (1957), 487–490 (in Russian) | MR | Zbl

[15] V. A. Andrunakievich, “Anti-simple and strongly idempotent rings”, Izv. Akad. Nauk SSSR Ser. Mat., 21:1 (1957), 15–144 (in Russian) | MR

[16] V. A. Andrunakievich, “Modular ideals, radicals and semisimplicity of rings”, Uspekhi Mat. Nauk, 12:3 (1957), 133–139 (in Russian) | MR | Zbl

[17] V. A. Andrunakievich, “Radicals of associative rings, I”, Mat. Sb., 44:2 (1958), 179–212 (in Russian) | MR

[18] V. A. Andrunakievich, “On the separation of the radical of a ring as a direct summand”, Uspehi Mat. Nauk, 13:5 (1958) (in Russian) | MR

[19] V. A. Andrunakievich, Radicals of associative rings, The thesis of the doctor of f. m. Sciences, Moscow State University, M., 1958 (in Russian) | MR

[20] V. A. Andrunakievich, “Radicals of weakly associative rings”, Dokl. Akad. Nauk SSSR, 134:6 (1960), 1271–1272 (in Russian) | MR

[21] V. A. Andrunakievich, “Radicals of weakly associative rings, I”, Izvestiya of Mold. Branch of the Academy of Sciences of the USSR, 10 (1960) | MR

[22] V. A. Andrunakievich, “Radicals of associative rings. II. Examples of special radicals”, Mat. Sbornik, 55:3 (1961), 329–346 (in Russian) | MR

[23] V. A. Andrunakievich, “On a characteristic of the supernilpotent radical”, Uspehi Mat. Nauk, 16:1 (1961), 127–130 (in Russian) | MR | Zbl

[24] V. A. Andrunakievich, “Prime modules and the Baer radical”, Sibirsk. Mat. Z., 2:6 (1961), 801–806 (in Russian) | MR | Zbl

[25] V. A. Andrunakievich, “Radicals of weakly associative rings, II. Special radicals”, Bul. Akad. Stiince RSS Moldova, 1962, no. 5, 3–9 (in Russian) | MR | Zbl

[26] V. A. Andrunakievich, “Radical and the decomposition of a ring”, Dokl. Akad. Nauk SSSR, 145:1 (1962), 9–12 (in Russian) | MR | Zbl

[27] V. A. Andrunakievich, “Radicals and the decomposition of a ring”, Theses of Int. Congress. Math. (Stockholm, 1962) | MR

[28] V. A. Andrunakievich, Yu. M. Ryabukhin, “Special modules and special radicals”, Dokl. Akad. Nauk SSSR, 147:6 (1962), 1274–1277 (in Russian) | MR | Zbl

[29] V. A. Andrunakievich, Yu. M. Ryabukhin, “On the embedding of the modules”, Dokl. Akad. Nauk SSSR, 153:3 (1963), 507–509 (in Russian) | MR | Zbl

[30] V. A. Andrunakievich, Yu. M. Ryabukhin, “Modules and radicals”, Dokl. Akad. Nauk SSSR, 156:4 (1964), 991–994 (in Russian) | MR | Zbl

[31] V. A. Andrunakievich, Yu. M. Ryabukhin, “Connected rings”, Dokl. Akad. Nauk SSSR, 162:6 (1965), 1219–1222 (in Russian) | MR | Zbl

[32] V. A. Andrunakievich, Yu. M. Ryabukhin, “Primary ideals are in noncommutative rings”, Dokl. Akad. Nauk SSSR, 165:1 (1965), 13–16 (in Russian) | MR | Zbl

[33] V. A. Andrunakievich, Yu. M. Ryabukhin, “To the additive theory of ideals in rings and modules”, Dokl. Akad. Nauk SSSR, 168:3 (1966), 495–498 (in Russian) | MR | Zbl

[34] V. A. Andrunakievich, Yu. M. Ryabukhin, “The general additive theory of ideals”, Theses of Int. Congress. Math. (Moscow, 1966)

[35] V. A. Andrunakievich, Yu. M. Ryabukhin, “Additive theory of ideals in systems with quotients”, Izv. Akad. Nauk SSSR, Ser. Mat., 31:5 (1967), 1057–1090 (in Russian) | MR | Zbl

[36] V. A. Andrunakievich, Yu. M. Ryabukhin, “Rings without nilpotent elements, and completely prime ideals”, Dokl. Akad. Nauk SSSR, 180:1 (1968), 9–11 (in Russian) | MR | Zbl

[37] V. A. Andrunakievich, Yu. M. Ryabukhin, “Direct sums of division algebras”, Dokl. Akad. Nauk SSSR, 189:5 (1969), 927–929 (in Russian) | MR | Zbl

[38] V. A. Andrunakievich, V. G. Marin, “Multi-operator linear algebras without nilpotent elements”, Dokl. Akad. Nauk SSSR, 197:4 (1971), 746–749 (in Russian) | MR | Zbl

[39] V. A. Andrunakievich, Yu. M. Ryabukhin, “Torsions in algebras”, Dokl. Akad. Nauk SSSR, 208:2 (1973), 265–268 (in Russian) | MR | Zbl

[40] V. A. Andrunakievich, Yu. M. Ryabukhin, “Radical closures of right ideals, and their complements”, Dokl. Akad. Nauk SSSR, 219:2 (1974), 268–271 (in Russian) | MR | Zbl

[41] V. A. Andrunakievich, Yu. M. Ryabukhin, “Certain classes of weakly Boolean rings”, Dokl. Akad. Nauk SSSR, 224:1 (1975), 11–14 (in Russian) | MR | Zbl

[42] V. A. Andrunakievich, K. K. Kracilov, Yu. M. Ryabukhin, “Radical closures in complete lattices. General theory”, Mat. Sb., 100:3 (1976), 339–355 (in Russian) | MR | Zbl

[43] V. A. Andrunakievich, K. K. Kracilov, Yu. M. Ryabukhin, “Lattice-complemented torsion in algebras over a Noetherian integral domain”, Dokl. Akad. Nauk SSSR, 242:5 (1978), 985–988 (in Russian) | MR | Zbl

[44] V. A. Andrunakievich, Yu. M. Ryabukhin, Radicals of algebras and structural theory, Nauka, M., 1979, 496 pp. (in Russian) | MR | Zbl

[45] V. A. Andrunakievich, I. D. Kitoroağa, Numere şi ideale, Lumina, Chisinau, 1979 (in Romanian)

[46] V. A. Andrunakievich, A. V. Andrunakievich, “Strictly modular ring ideals”, Dokl. Akad. Nauk SSSR, 257:1 (1981), 11–14 (in Russian) | MR | Zbl

[47] V. A. Andrunakievich, A. V. Andrunakievich, “One-sided ideals and ring radicals”, Dokl. Akad. Nauk SSSR, 259:1 (1981), 11–15 (in Russian) | MR | Zbl

[48] V. A. Andrunakievich, A. V. Andrunakievich, “One-sided ideals and radicals of rings”, Algebra i Logika, 20:5 (1981), 489–510 (in Russian) | MR | Zbl

[49] V. A. Andrunakievich, A. V. Andrunakievich, “Abelian-regular ring ideals”, Dokl. Akad. Nauk SSSR, 263 (1982), 1033–1036 (in Russian) | MR | Zbl

[50] V. A. Andrunakievich, A. V. Andrunakievich, “Subdirect products of division rings”, Dokl. Akad. Nauk SSSR, 269:4 (1983), 777–780 (in Russian) | MR | Zbl

[51] V. A. Andrunakievich, “Completely primary ideals of a ring”, Mat. Sb., 121:3 (1983), 291–296 (in Russian) | MR | Zbl

[52] V. A. Andrunakievich, A. V. Andrunakievich, “A completely semiprime maximal right ideal of a ring is two-sided”, Dokl. Akad. Nauk SSSR, 279:2 (1984), 270–273 (in Russian) | MR | Zbl

[53] V. A. Andrunakievich, Yu. M. Ryabukhin, “Free commutative quasiregular algebras and algebras without quasiregular subalgebras”, Uspekhi Mat. Nauk, 40:4 (1985), 131–132 (in Russian) | MR | Zbl

[54] V. A. Andrunakievich, Yu. M. Ryabukhin, “On varieties of quasiregular algebras”, Mat. Sb., 127:4 (1985), 419–444 (in Russian) | MR | Zbl

[55] V. A. Andrunakievich, Yu. M. Ryabukhin, “Varieties of quasiregular algebras”, Dokl. Akad. Nauk SSSR, 287:5 (1986), 1033–1036 (in Russian) | MR | Zbl

[56] V. A. Andrunakievich, Yu. M. Ryabukhin, “Primitivity and quasiregularity with respect to the right ideals of a ring”, Dokl. Akad. Nauk SSSR, 296:4 (1987), 777–780 (in Russian) | MR

[57] V. A. Andrunakievich, Yu. M. Ryabukhin, “Ideals relative to a right ideal $P$, and $C$-identities for $C\approx R/P$”, Izv. Akad. Nauk Moldav. SSR Mat., 1990, no. 2, 53–66 (in Russian) | MR | Zbl

[58] V. A. Andrunakievich, Yu. M. Ryabukhin, “Idempotents and quasiregularity with respect to right ideals of algebras”, Dokl. Akad. Nauk, 325:5 (1992), 889–892 (in Russian) | MR | Zbl

[59] V. A. Andrunakievich, Yu. M. Ryabukhin, “Minimal right ideals of a ring with respect to a fixed right ideal”, Dokl. Akad. Nauk, 331:6 (1993), 663–665 | MR | Zbl

[60] V. A. Andrunakievich, Yu. M. Ryabukhin, “On reduced right ideals of a ring”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 1995, no. 1, 74–77 | MR | Zbl

[61] Yu. M. Ryabukhin, “Quasiregular algebras, modules, groups, and varieties”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 1997, no. 1, 6–62 (in Russian) | MR

[62] N. Divinsky, Rings and radicals, Mathematical Exposition, 14, University of Toronto Press, Toronto, 1965, 160 pp. | MR

[63] K. A. Ževlakov, A. M. Slin'ko, I. P. Šeštakov, A. I. Širšov, Rings that are nearly associative, Nauka, M., 1978, 431 pp. (in Russian) | MR

[64] F. A. Szasz, Radicals of rings, A Wiley-Interscience Publication. John Wiley Sons, 1981, 287 pp. | MR | Zbl

[65] B. J. Gardner, R. Wiegandt, Radical Theory of Rings, Monographs and Textbooks in Pure and Applied Mathematics, 261, Marcel Dekker Inc., New York, 2004, 387 pp. | MR | Zbl