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Tadashi Nakayama (mathematician)
was a mathematician who made important contributions to representation theory. Career He received his degrees from Tokyo University and Osaka University and held permanent positions at Osaka University and Nagoya University. He had visiting positions at Princeton University, Illinois University, and Hamburg University. Nakayama's lemma, Nakayama algebras, Nakayama's conjecture In mathematics, Nakayama's conjecture is a conjecture about Artinian rings, introduced by . The generalized Nakayama conjecture is an extension to more general rings, introduced by . proved some cases of the generalized Nakayama conjecture. Nakaya ... and Murnaghan–Nakayama rule are named after him. Selected works * * * Tadasi Nakayama. A note on the elementary divisor theory in non-commutative domains. Bull. Amer. Math. Soc. 44 (1938) 719–723. * Tadasi Nakayama. A remark on representations of groups. Bull. Amer. Math. Soc. 44 (1938) 233–235. * Tadasi Nakayama. A remark on the sum and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tokyo Prefecture
Tokyo (; ja, 東京, , ), officially the Tokyo Metropolis ( ja, 東京都, label=none, ), is the capital and largest city of Japan. Formerly known as Edo, its metropolitan area () is the most populous in the world, with an estimated 37.468 million residents ; the city proper has a population of 13.99 million people. Located at the head of Tokyo Bay, the prefecture forms part of the Kantō region on the central coast of Honshu, Japan's largest island. Tokyo serves as Japan's economic center and is the seat of both the Japanese government and the Emperor of Japan. Originally a fishing village named Edo, the city became politically prominent in 1603, when it became the seat of the Tokugawa shogunate. By the mid-18th century, Edo was one of the most populous cities in the world with a population of over one million people. Following the Meiji Restoration of 1868, the imperial capital in Kyoto was moved to Edo, which was renamed "Tokyo" (). Tokyo was devastate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nakayama Algebra
In algebra, a Nakayama algebra or generalized uniserial algebra is an algebra such that each left or right indecomposable projective module has a unique composition series. They were studied by who called them "generalized uni-serial rings". These algebras were further studied by and later by , by and by . An example of a Nakayama algebra is ''k'' 'x''(''x''''n'') for ''k'' a field and ''n'' a positive integer. Current usage of ''uniserial'' differs slightly: an explanation of the difference appears here. References * * * * *{{Citation , last1=Reiten , first1=Idun , title=Representations of algebras (Puebla, 1980) , publisher=Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 ... , location=Berlin, New York , series=Lecture Notes in Mathematics , doi=10.1007/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Osaka University Alumni
is a designated city in the Kansai region of Honshu in Japan. It is the capital of and most populous city in Osaka Prefecture, and the third most populous city in Japan, following Special wards of Tokyo and Yokohama. With a population of 2.7 million in the 2020 census, it is also the largest component of the Keihanshin Metropolitan Area, which is the second-largest metropolitan area in Japan and the 10th largest urban area in the world with more than 19 million inhabitants. Osaka was traditionally considered Japan's economic hub. By the Kofun period (300–538) it had developed into an important regional port, and in the 7th and 8th centuries, it served briefly as the imperial capital. Osaka continued to flourish during the Edo period (1603–1867) and became known as a center of Japanese culture. Following the Meiji Restoration, Osaka greatly expanded in size and underwent rapid industrialization. In 1889, Osaka was officially established as a municipality. The con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1964 Deaths
Events January * January 1 – The Federation of Rhodesia and Nyasaland is dissolved. * January 5 - In the first meeting between leaders of the Roman Catholic and Orthodox churches since the fifteenth century, Pope Paul VI and Patriarch Athenagoras I of Constantinople meet in Jerusalem. * January 6 – A British firm, the Leyland Motor Corp., announces the sale of 450 buses to the Cuban government, challenging the United States blockade of Cuba. * January 9 – '' Martyrs' Day'': Armed clashes between United States troops and Panamanian civilians in the Panama Canal Zone precipitate a major international crisis, resulting in the deaths of 21 Panamanians and 4 U.S. soldiers. * January 11 – United States Surgeon General Luther Terry reports that smoking may be hazardous to one's health (the first such statement from the U.S. government). * January 12 ** Zanzibar Revolution: The predominantly Arab government of Zanzibar is overthrown by African nationalist rebels ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1912 Births
Year 191 ( CXCI) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Apronianus and Bradua (or, less frequently, year 944 ''Ab urbe condita''). The denomination 191 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Parthia * King Vologases IV of Parthia dies after a 44-year reign, and is succeeded by his son Vologases V. China * A coalition of Chinese warlords from the east of Hangu Pass launches a punitive campaign against the warlord Dong Zhuo, who seized control of the central government in 189, and held the figurehead Emperor Xian hostage. After suffering some defeats against the coalition forces, Dong Zhuo forcefully relocates the imperial capital from Luoyang to Chang'an. Before leaving, Dong Zhuo orders his troops to loot the tombs o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Murnaghan–Nakayama Rule
In group theory, a branch of mathematics, the Murnaghan–Nakayama rule, named after Francis Murnaghan and Tadashi Nakayama, is a combinatorial method to compute irreducible character values of a symmetric group.Richard Stanley, ''Enumerative Combinatorics, Vol. 2'' There are several generalizations of this rule beyond the representation theory of symmetric groups, but they are not covered here. The irreducible characters of a group are of interest to mathematicians because they concisely summarize important information about the group, such as the dimensions of the vector spaces in which the elements of the group can be represented by linear transformations that “mix” all the dimensions. For many groups, calculating irreducible character values is very difficult; the existence of simple formulas is the exception rather than the rule. The Murnaghan–Nakayama rule is a combinatorial rule for computing symmetric group character values χ using a particular kind of Young tab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nakayama's Conjecture
In mathematics, Nakayama's conjecture is a conjecture about Artinian rings, introduced by . The generalized Nakayama conjecture is an extension to more general rings, introduced by . proved some cases of the generalized Nakayama conjecture. Nakayama's conjecture states that if all the modules of a minimal injective resolution of an Artin algebra In algebra, an Artin algebra is an algebra Λ over a commutative Artin ring ''R'' that is a finitely generated ''R''-module. They are named after Emil Artin Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Arm ... ''R'' are injective and projective, then ''R'' is self-injective. References * * * Ring theory Conjectures {{abstract-algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nakayama's Lemma
In mathematics, more specifically abstract algebra and commutative algebra, Nakayama's lemma — also known as the Krull–Azumaya theorem — governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules. Informally, the lemma immediately gives a precise sense in which finitely generated modules over a commutative ring behave like vector spaces over a field. It is an important tool in algebraic geometry, because it allows local data on algebraic varieties, in the form of modules over local rings, to be studied pointwise as vector spaces over the residue field of the ring. The lemma is named after the Japanese mathematician Tadashi Nakayama and introduced in its present form in , although it was first discovered in the special case of ideals in a commutative ring by Wolfgang Krull and then in general by Goro Azumaya (1951). In the commutative case, the lemma is a simple consequence of a generalize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nagoya
is the largest city in the Chūbu region, the fourth-most populous city and third most populous urban area in Japan, with a population of 2.3million in 2020. Located on the Pacific coast in central Honshu, it is the capital and the most populous city of Aichi Prefecture, and is one of Japan's major ports along with those of Tokyo, Osaka, Kobe, Yokohama, and Chiba. It is the principal city of the Chūkyō metropolitan area, which is the third-most populous metropolitan area in Japan with a population of 10.11million in 2020. In 1610, the warlord Tokugawa Ieyasu, a retainer of Oda Nobunaga, moved the capital of Owari Province from Kiyosu to Nagoya. This period saw the renovation of Nagoya Castle. The arrival of the 20th century brought a convergence of economic factors that fueled rapid growth in Nagoya, during the Meiji Restoration, and became a major industrial hub for Japan. The traditional manufactures of timepieces, bicycles, and sewing machines were followe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
