Øystein Ore

Øystein Ore (7 October 1899 – 13 August 1968) was a Norwegianmathematician known for his work in ring theory, Galois connections, graph theory, and the history of mathematics.

Ore graduated from the University of Oslo in 1922, with a Cand.Real.degree in mathematics. In 1924, the University of Oslo awarded him the Ph.D. for a thesis titled Zur Theorie der algebraischen Körper, supervised by Thoralf Skolem.^[1] Ore also studied at Göttingen University, where he learned Emmy Noether's new approach to abstract algebra. He was also a fellow at the Mittag-Leffler Institute in Sweden, and spent some time at the University of Paris. In 1925, he was appointed research assistant at the University of Oslo.

Yale University’s James Pierpont went to Europe in 1926 to recruit research mathematicians. In 1927, Yale hired Ore as an assistant professor of mathematics, promoted him to associate professor in 1928, then to full professor in 1929. In 1931, he became a Sterling Professor (Yale's highest academic rank), a position he held until he retired in 1968.

Ore gave an American Mathematical Society Colloquium lecture in 1941 and was a plenary speaker at the International Congress of Mathematicians in 1936 in Oslo. He was also elected to the American Academy of Arts and Sciences and the Oslo Academy of Science. He was a founder of the Econometric Society.

Ore visited Norway nearly every summer. During World War II, he was active in the "American Relief for Norway" and "Free Norway" movements. In gratitude for the services rendered to his native country during the war, he was decorated in 1947 with the Order of St. Olav.

In 1930, Ore married Gudrun Lundevall. They had two children. Ore had a passion for painting and sculpture, collected ancient maps, and spoke several languages.

Ore is known for his work in ring theory, Galois connections, and most of all, graph theory.

His early work was on algebraic number fields, how to decompose the ideal generated by a prime number into prime ideals. He then worked on noncommutative rings, proving his celebrated theorem on embedding a domain into a division ring. He then examined polynomial rings over skew fields, and attempted to extend his work on factorisation to non-commutative rings. The Ore condition, which (if true) allows a ring of fractions to be defined, and the Ore extension, a non-commutative analogue of rings of polynomials, are part of this work. In more elementary number theory, Ore's harmonic numbers are the numbers whose divisors have an integer harmonic mean.

As a teacher, Ore is notable for supervising two doctoral students who would make contributions to science and mathematics: Grace Hopper, who eventually became a United Statesrear admiral and computer scientist and who was a pioneer in developing the first computers, and Marshall Hall, Jr., an American mathematician who did important research in group theory and combinatorics.

In 1930, the Collected Works of Richard Dedekind were published in three volumes, jointly edited by Ore and Emmy Noether. He then turned his attention to lattice theory becoming, together with Garrett Birkhoff, one of the two founders of American expertise in the subject. Ore's early work on lattice theory led him to the study of equivalence and closure relations, Galois connections, and finally to graph theory, which occupied him to the end of his life. He wrote two books on the subject, one on the theory of graphs and another on their applications. Within graph theory, Ore's theorem is one of several results proving that sufficiently dense graphs contain Hamiltonian cycles.

Ore had a lively interest in the history of mathematics, and was an unusually able author of books for laypeople, such as his biographies of Cardano and Niels Henrik Abel.

• Les Corps Algébriques et la Théorie des Idéaux (1934)
• L'Algèbre Abstraite (1936)
• Number Theory and its History (1948)
• Cardano, el erudito del juego (Princeton University Press, 1953)
• Niels Henrik Abel, matemático extraordinario (Editorial de la Universidad de Minnesota, 1957)
• Teoría de grafos (1962)
• Gráficos y sus usos (1963)
• El problema de los cuatro colores (1967)
• Invitación a la teoría de números (1969)

• "Sobre los fundamentos del álgebra abstracta (1)". Ann. of Math. 36 (2): 406– 406. Abril de 1935. doi : 10.2307/1968580 . JSTOR 1968580 . 
• "Sobre los fundamentos del álgebra abstracta (2)". Ann. of Math . 37 (2): 265– 292. Abr 1936. doi : 10.2307/1968442 . JSTOR 1968442 . 
• "Estructuras y teoría de grupos (1)" . Duke Math. J. 3 (2): 149– 174. Junio ​​de 1937. doi : 10.1215/S0012-7094-37-00311-9 .
• "Estructuras y teoría de grupos (2)" . Duke Math. J. 4 ( 2): 247– 269. Junio ​​de 1938. doi : 10.1215/S0012-7094-38-00419-3 .
• "Observaciones sobre estructuras y relaciones grupales". Vierteljschr. Naturalmente. Ges. Zúrich, Beiblatt Festschrift Rudolf Fueter . 85 : 1–4 . 1940.
• "Teoría de las relaciones de equivalencia" . Duke Math. J. 9 ( 3): 573– 627. Sep 1942. doi : 10.1215/S0012-7094-42-00942-6 .
• "Cadenas en conjuntos parcialmente ordenados" . Bull. Amer. Math. Soc. 49 (8): 558– 566. 1943. doi : 10.1090/S0002-9904-1943-07970-0 .
• "Combinaciones de relaciones de cierre". Ann. of Math . 44 (3): 514– 533. Jul 1943. doi : 10.2307/1968978 . JSTOR 1968978 . 
• "Conexiones Galois" . Trans. América. Matemáticas. Soc. 55 : 493– 513. 1944. doi : 10.1090/S0002-9947-1944-0010555-7 .

• Deficiencia (teoría de grafos)
• Gráfico geodésico
• Magma (álgebra)
• Álgebra mineral
• Estado del mineral
• La conjetura de Ore
• Extensión de mineral
• Número de mineral
• Teorema de Ore
• Lema de Schwartz-Zippel
• Álgebra universal

• O'Connor, John J.; Robertson, Edmund F. , "Øystein Ore" , Archivo MacTutor de Historia de las Matemáticas , Universidad de St Andrews. La fuente de gran parte de esta entrada.