algebraとは 意味・読み方・使い方

発音

• (英国発音) IPA^(key): /ˈæl.dʒɪ.bɹə/
• (米国発音) IPA^(key): /ˈæl.d͡ʒɪ.bɹə/, /ˈæl.d͡ʒə.bɹə/
• 韻: -iːbɹə

名詞

algebra (countable かつ uncountable, 複数形 algebras)

1. (uncountable, mathematics) A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
   • 1551, James A.H. Murray, editor, A New English Dictionary on Historical Principles: Founded Mainly on the Materials Collected by the Philological Society.‎^[2], volume 1, Oxford: Clarendon Press, published 1888, Part 1, page 217:

     Also the rule of false position, with dyuers examples not only vulgar, but some appertaynyng to the rule of Algeber.

   • 1854, George Boole, “Signs and their Laws”, in An Investigation of the Laws of Thought, on which are Founded the Mathematical Theories of Logic and Probabilities‎^[3], London: Walton and Maberly, page 37:

     Let us conceive, then, of an Algebra in which the symbols x, y, z, &c. admit indifferently of the values 0 and 1, and of these values alone.

2. (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
   • a1420, The British Museum Additional MS, 12,056, “Wounds complicated by the Dislocation of a Bone”, in Robert von Fleischhacker, editor, Lanfranc's "Science of cirurgie."‎^[4], London: K. Paul, Trench, Trübner & Co, translation of original by Lanfranc of Milan, published 1894, →ISBN, page 63:

     Ne take noon hede to brynge togidere þe parties of þe boon þat is to-broken or dislocate, til viij. daies ben goon in þe wyntir, & v. in þe somer; for þanne it schal make quytture, and be sikir from swellynge; & þanne brynge togidere þe brynkis eiþer þe disiuncture after þe techynge þat schal be seid in þe chapitle of algebra.

   • 1987, John Newsome Crossley, “Latency”, in The emergence of number‎^[5], Singapore: World Scientific, →ISBN, Al-Khwarizwi, page 65:

     Algebra is used today by surgeons to mean bone-setting, i.e. the restoration of bones, and the idea of restoration is present in the mathematical context, too.

3. (uncountable, mathematics) The study of algebraic structures.
4. (countable, mathematics) A universal algebra.
5. (countable, algebra) An algebraic structure consisting of a module over a commutative ring (または a vector space over a field) along with an additional binary operation that is bilinear over module (または vector) addition and scalar multiplication.

   Synonyms: algebra over a field, algebra over a ring

   • 2018 March 23, Wikipedia contributors, “Lie algebra”, in English Wikipedia‎^[6], Wikimedia Foundation, revision 831953572:

     In mathematics, a Lie algebra (pronounced /liː/ "Lee") is a vector space ${\displaystyle {\mathfrak {g}}}$ together with a non-associative, alternating bilinear map ${\displaystyle {\mathfrak {g}}\times {\mathfrak {g}}\rightarrow {\mathfrak {g}};(x,y)\mapsto [x,y]}$, called the Lie bracket, satisfying the Jacobi identity.

6. (countable, set theory, mathematical analysis) A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (かつ thereby also under intersections かつ differences).

   Synonyms: field of sets, algebra of sets

   Hypernym: ring

   Hyponym: σ-algebra

7. (countable, mathematics) One of several other types of mathematical structure.
8. (figurative) A system or process, that is like algebra by substituting one thing for another, or in using signs, symbols, etc., to represent concepts or ideas.
   • 1663, William Clark, William Hugh Logan, editor, Marciano; or, The discovery: A tragi-comedy‎^[7], Edinburgh: Reprinted for Private Circulation, published 1871, →ISBN, page 13:

     Fly ! Fly ! avaunt with that base cowardly gibbrish ; That Algebra of honour ; which had never Been nam'd, if all had equal courage—what?

派生語

関連する語

アナグラム

• Labarge

Latin

語源

Borrowed from Arabic الْجَبْر‎ (al-jabr, “reunion, resetting of broken parts”).

発音

• (Classical) IPA^(key): /ˈal.ɡe.bra/, [ˈäɫ̪ɡɛbrä]
• (Ecclesiastical) IPA^(key): /ˈal.d͡ʒe.bra/, [ˈäl̠ʲd͡ʒebrä]

名詞

algebra f (genitive algebrae); first declension

1. (Medieval Latin, New Latin) algebra

語形変化

First-declension noun.

参照

• algebra in Charles du Fresne du Cange’s Glossarium Mediæ et Infimæ Latinitatis (augmented edition with additions by D. P. Carpenterius, Adelungius かつ others, edited by Léopold Favre, 1883–1887)