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Bredikhin D. A., Makeev N. N., Poplavski V. B. Legacy of Viktor Wagner. On the 90th anniversary of the Department of Geometry of Saratov State University. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 3, pp. 442-453. DOI: 10.18500/1816-9791-2025-25-3-442-453, EDN: EVXYVR
Legacy of Viktor Wagner. On the 90th anniversary of the Department of Geometry of Saratov State University
The article is dedicated to the 90th anniversary of the Department of Geometry of Saratov State University, which was founded by the outstanding mathematician, honored scientist Viktor Vladimirovich Wagner. A brief description of the scientific work of V. V. Wagner and the main achievements in the field of geometry, algebra, and their applications is given. Prospects for further development of the scientific research areas founded by him are noted.
- Wagner V. V. Sur la géométrie différentielle des multiplicities anholonomes. Trudy seminara po vektornomu i tenzornomu analizu [Proceedings of the Seminar on Vector and Tensor Analysis], 1935, iss. 2–3, pp. 269–318 (in French).
- Liber A. E., Penzov Yu. E., Rashevsky P. K. Viktor Vladimirovich Wagner (on the 50th anniversary of his birth). Russian Mathematical Surveys, 1958, vol. 13, iss. 6 (84), pp. 221–227 (in Russian).
- Efimov N. V., Liber A. E., Lyapin E. S., Rashevskii P. K. Viktor Vladimirovich Wagner (on his seventieth birthday). Russian Mathematical Surveys, 1979, vol. 34, iss. 4, pp. 209–212. DOI: 10.1070/RM1979v034n04ABEH003268
- Rozen V. V. (ed.) Viktor Vladimirovich Wagner. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2008, vol. 8 (separate print). 41 p. (in Russian).
- Dobronravov V. V. Osnovy mekhaniki negolonomnykh sistem [Fundamentals of mechanics of nonholonomic systems]. Moscow, Vysshaya shkola, 1970. 272 p. (in Russian).
- Liber A. E., Losik M. V., Penzov Yu. E. Viktor Vladimirovich Wagner (on the 70th anniversary of his birth). Differential Geometry, 1979, iss. 4, pp. 3–14 (in Russian).
- Grigoryan A. T., Fradlin B. N. Istoriya mekhaniki tvyordogo tela [History of Solid Mechanics]. Moscow, Nauka, 1982. 294 p. (in Russian).
- Wagner V. V. Geometrical interpretation of motion of nonholonomic dynamic systems. Trudy seminara po vektornomu i tenzornomu analizu [Proceedings of the Seminar on Vector and Tensor Analysis], 1941, iss. 5, pp. 173–225 (in Russian).
- Wagner V. V. The theory of a field of local hyperbands in Xn and its applications to the mechanics of a system with nonholonomic constraints. Doklady Akademii Nauk SSSR, 1949, vol. 66, iss. 6, pp. 1033–1036. (in Russian).
- Dobronravov V. V. Control systems with nonholonomic constraints. Mekhanika [Mechanics]. Collected papers. Moscow, Oborongiz, 1961, iss. 104, pp. 27–32 (in Russian).
- Sedov L. I., Èglit M. È. Construction of nonholonomic models of continuous media with allowance for the finite nature of deformations and certain physico-chemical effects. Doklady Akademii Nauk SSSR, 1962, vol. 142, iss. 1, pp. 54–57 (in Russian).
- Wagner V. V. Generalized groups. Doklady Akademii Nauk SSSR, 1952, vol. 84, iss. 6, pp. 1119-1122 (in Russian).
- Wagner V. V. Representation of ordered semigroups. Sbornik: Mathematics, 1956, vol. 38, iss. 2, pp. 203–240 (in Russian).
- Liber A. E. On the theory of generalized groups. Doklady Akademii Nauk SSSR, 1954, vol. 97, iss. 1, pp. 25–28 (in Russian).
- Clifford A., Preston G. Algebraicheskaya teoriya polugrupp [The algebraic theory of semigroups]. Vol. 2. Moscow, Mir, 1972. 422 p. (in Russian).
- Mitsch H. A natural partial order for semigroups. Proceedings of the American Mathematical Society, 1986, vol. 97, iss. 3, pp. 384–388. DOI: https://doi.org/10.1090/S0002-9939-1986-0840614-0
- Hartwig R. How to partially order regular elements. Mathematica Japonica, 1980, vol. 25, iss. 1, pp. 1–13.
- Nambooripad K. S. S. The natural partial order on a regular semigroup. Proceedings of the Edinburgh Mathematical Society, 1980, vol. 23, iss. 3, pp. 249–260. DOI: https://doi.org/10.1017/S0013091500003801
- Mitsch H. Semigroups and their natural order. Mathematica Slovaca, 1986, vol. 44, iss. 4, pp. 445-462.
- Poplavski V. B. Partial orders and idempotents of monoids. Chebyshevskii Sbornik, 2021, vol. 22, iss. 4, pp. 182–198 (in Russian). DOI: https://doi.org/10.22405/2226-8383-2021-22-4-182-198, EDN: UZQNWZ
- Jonsson B. Representation of modular lattices and of relation algebras. Transactions of the American Mathematical Society, 1959, vol. 92, pp. 449–464. DOI: https://doi.org/10.1090/S0002-9947-1959-0108459-5
- Andréka H., Bredikhin D. A. The equational theory of union-free algebras of relations. Algebra Universalis, 1994, vol. 33, pp. 516–532. DOI: https://doi.org/10.1007/BF01225472
- Schein B. M. Relation algebras and function semigroups. Semigroup Forum, 1970, vol. 1, pp. 1–62. DOI: https://doi.org/10.1007/BF02573019, EDN: XLNTYL
- Shain B. M. Imbedding of semigroups in generalized groups. Sbornik: Mathematics, 1961, vol. 55, iss. 4, pp. 379–400 (in Russian).
- Wagner V. V. Theory of relations and algebra of partial maps. In: Teoriya polugrupp i ee prilozheniya [Theory of Semigroups and Its Applications]. Saratov, Saratov State University Publ., 1965, iss. 1, pp. 3–178 (in Russian).
- Rozen V. V. (ed.) Professor Wagner’s School. Department of Geometry of Saratov University. Saratov, Saratov State University Publ., 2020. 328 p. (in Russian).
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