To the 90th anniversary of the birth of A. I. Kokorin. Stages of scientific and pedagogical way
The Bulletin of Irkutsk State University. Series Mathematics, Tome 29 (2019), pp. 138-154
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The paper is devoted to the scientific and pedagogical activity of A. I. Kokorin, the founder of the Irkutsk algebraic-logical school, whose 90th anniversary is celebrated in November 2019. Five research areas with the most significant contributions made by A. I. Kokorin are described. A brief overview of his achievements in each area is established. A list of publications, as well as that of dissertations, defended under supervising by A. I. Kokorin is given.
Keywords: ordered groups, extended theories, decidability.
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V. V. Bludov; N. A. Peryazev; S. F. Vinokurov; V. I. Panteleev. To the 90th anniversary of the birth of A. I. Kokorin. Stages of scientific and pedagogical way. The Bulletin of Irkutsk State University. Series Mathematics, Tome 29 (2019), pp. 138-154. http://geodesic.mathdoc.fr/item/IIGUM_2019_29_a11/

[1] A. I. Kokorin (red.), Algebra, IGU Publ., Irkutsk, 1972, 135 pp. (in Russian)

[2] A. I. Kokorin (red.), Algebra, 2, IGU Publ., Irkutsk, 1973, 164 pp. (in Russian)

[3] A. I. Kokorin (red.), Algebraic systems, IGU Publ., Irkutsk, 1976, 169 pp. (in Russian)

[4] A. I. Kokorin (red.), Algorithmic problems of algebraic systems, IGU Publ., Irkutsk, 1978, 217 pp. (in Russian)

[5] A. I. Kokorin (red.), Algorithmic problems of algebraic systems and computers, IGU Publ., Irkutsk, 1979, 224 pp. (in Russian)

[6] A. I. Kokorin (ed.), Algorithmic problems of algebraic systems and computers, IGU Publ., Irkutsk, 1985, 152 pp. (in Russian)

[7] A. I. Kokorin (red.), Algebraic system. Algorithmic problems and computers, IGU Publ., Irkutsk, 1986, 178 pp. (in Russian) | MR

[8] Bludov V. V., “Uniquely orderable groups”, Algebra and Logic, 13:6 (1974), 343–360 | MR | Zbl

[9] Bludov V. V., Some questions of orderable group theory, Cand. Sci. Phys.-Math. Dissertation, Novosibirsk, 1975, 106 pp. (in Russian)

[10] Bludov V. V., Kokorin A. I., “Semihomogeneously lattice-ordered groups”, Algebraicheskie sistemy, IGU Publ., Irkutsk, 1976, 3–16 (in Russian)

[11] Bludov V. V., Kokorin A. I., “T-generically ordered groups”, Sib. Math. J., 20:6 (1979), 868–872 ; 110 | MR | MR | Zbl

[12] Bludov V. V., Kokorin A. I., “Use of computers in solving well-known algebra problems”, Cybernetics, 18 (1982), 819–829 | MR

[13] Bludov V. V., Lapshina E. S., “On ordering of groups with nilpotent commutator subgroup”, Siberian Math. J., 44:3 (2003), 405–410 | MR | Zbl

[14] Boldonov V. I., Object modeling and functional universality in database construction tasks, Cand. Sci. Tech. Dissertation, Irkutsk, 1983, 157 pp. (in Russian)

[15] Boldonov V. I., Kokorin A. I., Penzin Ju. G., “Approach to automation of course exams in mathematics”, Algoritmicheskie voprosy algebraicheskih sistem, mezhvuz. sb., Irkutsk, 1978, 3–8 (in Russian)

[16] Vasil'ev Ju. P., The application of computers and questions of factorization in the group theory, Extended Abstract of Cand. Sci. Phys.-Math. Dissertation, Novosibirsk, 1975, 17 pp. (in Russian)

[17] Gurevich Ju. Sh., Kokorin A. I., “Universal equivalence of ordered Abelian groups”, Algebra i logika, 2:1 (1963), 37–39 (in Russian) | MR | Zbl

[18] Dulatova Z. A., The algorithmic questions in Boolean algebras, Cand. Sci. Phys.-Math. Dissertation, Irkutsk, 1987, 98 pp. (in Russian) | Zbl

[19] Kargapolov M. I., Kokorin A. I., Kopytov V. M., “On the theory of orderable groups”, Algebra i logika. Seminar, 4, no. 6, Novosibirsk, 1965, 21–27 (in Russian) | MR | Zbl

[20] Klejmenov V. F., Automorphisms of some classes of ordered groups, Cand. Sci. Phys.-Math. Dissertation, Irkutsk, 1986, 92 pp. (in Russian)

[21] Kozlov G. T., On the theory of Abelian groups, Cand. Sci. Phys.-Math. Dissertation, Novosibirsk, 1970, 56 pp. (in Russian)

[22] Kozlov G. T., Kokorin A. I., “Expanded elementary and universal theories of lattice-ordered abelian groups with a finite number of fibers”, Algebra and Logic, 7:1 (1968), 54–61 | MR | Zbl

[23] Kozlov G. T., Kokorin A. I., “Elementary theory of abelian groups without torsion, with a predicate selecting a subgroup”, Algebra and Logic, 8:3 (1969), 182–190 | MR

[24] Kozlov G. T., Kokorin A. I., Fridman Je. I., “Extended elementary theories of lattice-ordered abelian groups”, IX Vsesojuznyj algebraicheskij kollokvium, rez. nauch. soobshh. (ijul' 1968, g. Gomel'), 1968, 95–96 (in Russian)

[25] Kozlov G. T., Kokorin A. I., “Proof of a lemma on model completeness”, Algebra and Logic, 14:5 (1975), 328–330 | MR | Zbl

[26] Kokorin A. I., “On groups ordered in a unique way”, Doklady Vtoroj Sibirskoj konferencii po matematike i mehanike, Tomsk, 1962, 87–88 (in Russian)

[27] Kokorin A. I., “On a class of lattice-ordered groups”, Matematicheskie zapiski, 3, no. 3, Sverdlovsk, 1962, 37–38 (in Russian) | MR

[28] Kokorin A. I., Questions of group ordering, Extended Abstract of Cand. Sci. Phys.-Math. Dissertation, Sverdlovsk, 1963, 7 pp. (in Russian)

[29] Kokorin A. I., “Complete orderability of the direct product of completely orderable groups”, Matematicheskie zapiski, 4, no. 3, Sverdlovsk, 1963, 95–96 (in Russian) | MR | Zbl

[30] Kokorin A. I., “Toward a theory of fully orderable groups”, Matematicheskie zapiski, 4, no. 3, Sverdlovsk, 1963, 25–29 (in Russian) | MR | Zbl

[31] Kokorin A. I., “Toward a theory of completely orderable groups”, Algebra i logika. Seminar, 2, no. 6, Novosibirsk, 1963, 15–20 (in Russian) | MR | Zbl

[32] Kokorin A. I., “On completely orderable groups”, Dokl. AN SSSR, 151:1 (1963), 31–33 (in Russian) | MR | Zbl

[33] Kokorin A. I., “Methods of lattice ordering of a free Abelian group with a finite number of generators”, Matematicheskie zapiski, 4, no. 1, Sverdlovsk, 1963, 45–48 (in Russian) | MR | Zbl

[34] Kokorin A. I., “$\Gamma$-Completely orderable and relatively convex subgroups of orderable groups”, Sib. Math. J., 7:3 (1966), 570–572 | MR | Zbl

[35] Kokorin A. I., Orderable Groups, NGU Publ., Novosibirsk, 1966, 128 pp. (in Russian)

[36] Kokorin A. I., “Intersection and union of relatively convex subgroups of ordered groups”, Algebra and Logic, 7:3 (1968), 160–161 | MR | Zbl

[37] Kokorin A. I., Mathematical logic and algorithms, Angarsk, 1972, 44 pp. (in Russian)

[38] Kokorin A. I., “Extended theories and relative decidability”, Pjataja Vsesojuznaja konferencija po matematicheskoj logike, posvjashhennaja 70-letiju akademika A. I. Mal'ceva, tez. dokl. (Novosibirsk, 27–29 nojab. 1979), 1979, 68

[39] Kokorin A. I., “Relative decidability of multi-core models”, XVI Vsesojuznaja algebraicheskaja konferencija, tezisy (Leningrad, 22–25 sent. 1981 g.), v. 1, 1981, 75 pp. (in Russian)

[40] Kokorin A. I., “Connection of decidability questions and evaluation of the SPF method for optimal strategy construction”, Problemy teoreticheskoj kibernetiki, tez. dokl. Sed'moj Vsesojuz. konf. (Irkutsk, 18–20 sent. 1985), v. 1, 96 (in Russian)

[41] Kokorin A. I., “Mathematical model of transition from polytheism to monotheism”, Logika i sistemnye metody analiza nauchnogo znanija, tezisy dokladov k IX Vsesojuznomu soveshhaniju po logike, metodologii i filosofii nauki, Sekcii 1–5 (Har'kov), M., 1986, 198–200 (in Russian)

[42] Kokorin A. I., Kopytov V. M., “On some classes of orderable groups”, Algebra i logika. Seminar, 1, no. 3, Novosibirsk, 1962, 21–23 (in Russian) | MR | Zbl

[43] Kokorin A. I., Kopytov V. M., “Relative convexity of generalized centers of orderable groups”, Matematicheskie zapiski, 5, no. 1, Sverdlovsk, 1965, 49–53 (in Russian) | MR | Zbl

[44] Kokorin A. I., Kopytov V. M., “Relatively convex subgroups of orderable groups”, Trudy Mezhdunarodnogo kongressa matematikov, sekcija 2, tez. krat. nauch. soobshh. (Moskva, 16–26 avg. 1966 g.), M., 1966, 44 (in Russian)

[45] Kokorin A. I., Kopytov V. M., “Relatively convex subgroups of orderable groups”, Sib. Math. J., 9:4 (1968), 622–628 | MR | Zbl

[46] Kokorin A. I., Kopytov V. M., Fully Ordered Groups, J. Wiley $\$ Sons, New York, 1974, 147 pp. | MR

[47] Kokorin A. I., Mart'janov V. I., “On universal extended theories”, XII Vsesojuznyj algebraicheskij kollokvium, tez. soobshh. (Sverdlovsk, 1973), v. 1, 26 (in Russian)

[48] Kokorin A. I., Mart'janov V. I., “Universal extended theories”, Algebra, 2, Irkutsk, 1973, 107–113 (in Russian) | MR

[49] Kokorin A. I., Mart'janov V. I., “Connections in universal extended theories”, Tret'ja Vsesojuznaja konferencija po matematicheskoj logike, tez. dokl. (23–27 ijunja 1974, Novosibirsk), 1974, 113 (in Russian)

[50] Kokorin A. I., Mart'janov V. I., Fridman Je. I., “Relative decidability and extended theories”, 14-ja Vsesojuznaja algebraicheskaja konferencija, tez. dokl. (Novosibirsk, 1977), v. 2, Kol'ca. Algebraicheskie sistemy, 103 (in Russian) | Zbl

[51] Kokorin A. I., Pinus A. G., “Decidability problems of extended theories”, Russian Mathematical Surveys, 33:2 (1978), 53–96 | MR | Zbl

[52] Kokorin A. I., Tarasova V. P., “Mathematical model of transition from polytheism to monotheism”, Algebra, logika i prilozhenija, sb. nauch. tr., IGU Publ., Irkutsk, 1994, 5–14 (in Russian)

[53] Kokorin A. I., Fridman Je. I., “Decidability of element-convex-subgroups-theories of ordered and orderable abelian groups”, Materialy nauchnoj konferencii za 1969–1970 gg., Matematika, geografija, geologija, 2, Irkutsk, 1970, 56–57 (in Russian)

[54] Kokorin A. I., Fridman Je. I., “Extended theories of abelian groups”, Materialy Vos'moj mezhvuzovskoj matematicheskoj nauchnoj konferencii Dal'nego Vostoka (Habarovsk, 1970), 15–16 (in Russian) | MR

[55] Kokorin A. I., Fridman Je. I., “Element-serving-subgroup-theory of abelian groups”, XI Vsesojuznyj algebraicheskij kollokvium, rez. soobshh. i dokl. (Kishinev, 1971), 46 (in Russian)

[56] Kokorin A. I., Fridman Je. I., “Application of the decidability problems”, Algoritmicheskie voprosy algebraicheskih sistem i JeVM, sb. nauch. tr. (Irkutsk, 1979), 84–96 (in Russian) | Zbl

[57] Kokorin A. I., Hisamiev N. G., “Elementary classification of lattice-ordered Abelian groups with a finite number of fibers”, Algebra i logika, 5:1 (1966), 41–50 (in Russian) | MR | Zbl

[58] Kontorovich P. G., Kokorin A. I., “On a type of partially ordered groups”, Matematicheskie zapiski, 3, no. 3, Sverdlovsk, 1962, 39–44 (in Russian)

[59] Kontorovich P. G., “Zasedanija Ural'skogo matematicheskogo obshhestva”, Zasedanie 14 nojabrja 1962 g. po teme «Ob uporjadochennyh gruppah» [On orderable groups]. Avtor doklada A. I. Kokorin. p. 215, Uspehi mat. nauk, 19:2 (1964), 209–223 (in Russian)

[60] Kopytov V. M., Lattice-ordered groups, Nauka Publ., M., 1984, 320 pp. (in Russian) | MR

[61] Kopytov V. M., “Groups of Formal Power Series Are Fully Orderable”, Algebra and Logic, 37:3 (1998), 170–180 | MR | Zbl

[62] Kopytov V. M., Medvedev N. Ya., Right-ordered Groups, Plenum Publ. Corp., New York, 1996, 250 pp. | MR

[63] Mancivoda A. V., Abstract data types and the automatic theorem proving, Cand. Sci. Phys.-Math. Dissertation, Irkutsk, 1988, 121 pp. (in Russian) | Zbl

[64] Mart'janov V. I., Element-subgroup theories of Abelian groups with automorphism, Cand. Sci. Phys.-Math. Dissertation, Irkutsk, 1979, 90 pp. (in Russian)

[65] Unsolved Problems in mathematical logic. The Logical Notebook, IM SO AN SSSR Publ., Novosibirsk, 1986 (in Russian)

[66] Unsolved Problems in Group Theory, The Kourovka Notebook, 15, Institute of Mathematics SO RAN Publ., Novosibirsk, 2002

[67] Unsolved Problems in the theory of rings and modules, The Dnestr Notebook, IM SO AN SSSR Publ., Novosibirsk, 1969 (in Russian)

[68] Penzin Ju. G., The algorithmic questions of number theory, Cand. Sci. Phys.-Math. Dissertation, Irkutsk, 1975, 67 pp. (in Russian)

[69] Perjazev N. A., Indiscernibility, completeness and decidability of positive theories, Cand. Sci. Phys.-Math. Dissertation, Irkutsk, 1987, 87 pp. (in Russian)

[70] Slobodskoj A. M., The questions of decidability of the universal and extended theories, Cand. Sci. Phys.-Math. Dissertation, Irkutsk, 1980, 106 pp. (in Russian) | Zbl

[71] Fridman Je. I., Extended and restricted theories of Abelian groups and lattices, Cand. Sci. Phys.-Math. Dissertation, Irkutsk, 1981, 133 pp. (in Russian)

[72] Fuchs L., Partially Ordered Algebraic Systems, Pergamon Press, New York, 1963, 229 pp. | MR | Zbl

[73] Hisamiev N. G., The questions of elementary theory of lattice-ordered algebraic systems, Cand. Sci. Phys.-Math. Dissertation, Novosibirsk, 1968 (in Russian)

[74] Bludov V. V., Glass A. M. W., Kopytov V. M., Medvedev N. Ya., Unsolved Problems in Ordered and orderable Groups, 2009, 27 pp., arXiv: 0906.26211v1 [math.GR] | MR

[75] Dlab V., “On a family of simple ordered groups”, J. Austral. Math. Soc., 8:3 (1968), 591–608 | DOI | MR | Zbl

[76] Glass A. M. W., Partially Ordered Groups, Series in Algebra, 7, World Scientific, Singapore, 1999, 324 pp. | MR | Zbl

[77] Kokorin A. I., “Mathematical model of transition from polytheism to monotheism”, 8 International congress of logic, methodology and philosofy of science, section 2 (Moscow, Aug. 17–22, 1987), v. 1, M., 98–100

[78] Kopytov V. M., Medvedev N. Ya., The theory of lattice-ordered groups, Kluwer Academic Publ, Dordrecht, 1994, 400 pp. | DOI | MR | Zbl

[79] Longobardi P., Maj M., Rhemtulla A. H., “On solvable $R^\ast$-groups”, J. Group Theory, 6:4 (2003), 499–503 | DOI | MR | Zbl

[80] Mura R. B, Rhemtulla A. H., Orderable groups, Lecture Notes in Pure and Applied Mathematics, 27, Marcel Dekker, New York, 1977, 169 pp. | MR