Algebra homologica

[thumb|upright=1.6|Diagramma [lemma anguinum|lemmatis anguini, unius ex exitibus fundamentalibus in algebra homologica]]
**Algebra homologica** est campus mathematicae, quae homologiam in generali spatio algebraico investigat. Est disciplina aliquantum iuvenis, exoriens ex investigationibus in topologia combinatoriali (praecursore topologiae algebraicae) et algebra abstracta (theoria modulorum et syzygiarum) praecipue ab Henrico Poincaré et Davidis Hilbert saeculo undevicensimo exeunte factis.

Progressus in algebra homologica cum theoria categoriarum orta artissime conexus est. Algebra homologica mox est studium functorum homologicorum et structurarum contortarum, quas efficiunt. Certa notio ubique praesens, una ex notionibus utilissimis in mathematica, est notio complexionum catenarum, quae per ambas earum homologiam et cohomologiam investigari potest. Algebra homologica modum praebet datorum extrahendorum, quae in his complexionibus continentur et horum datorum offerendorum in forma homologicorum invariantium anulorum, modulorum, spatiorum topologicorum, aliarumque rerum mathematicarum, qui ut dicuntur tangi possunt. Instrumentum potens harum rerum faciendarum per sequentias spectrales praebetur.

Algebra homologica partes magni momenti in topologia algebraica semper egit. Eius auctoritas gradatim crevit, et hodie algebram commutativam, geometriam algebraicam, theoriam numerorum algebraicam, theoriam representationis, physicam mathematicam, algebram operatorum, explicationem multiplicem, et theoriam aequationum differentialium partialium comprehendit. Theoria-K est disciplina soluta, quae autem rationibus algebrae homologicae utitur, sicut et geometria incommutativa Alani Connes.

## Historia algebrae homologicae
Algebra homologica investigari coepit saeculo undevicensimo ut ramus topologiae, sed solum annis 1940 facta est res soluta in studio rerum sicut ext functoris ext et functoris tor, ut sic appellantur.

*Algebra homotopica
*Anulus (mathematica)
*Derivator
*Homotopia
*Isomorphismus
*Lemma soleae
*Nugae abstractae
*Polynomium
*Theorema fundamentale algebrae
*Topologia algebraica

## Notae
## Bibliographia
*André, M. (Michel). 1967. *Méthode simpliciale en algèbre homologique et algèbre commutative.* Berolini et Novi Eboraci: Springer-Verlag.
*Cartan, Henri, et Samuel Eilenberg. (1955) 1999. *Homological algebra.* Cum appendice a David A. Buchsbaum scripta. Princeton Landmarks in Mathematics. Princetoniae: Princeton University Press. ISBN 0-691-04991-2.
*Gelfand, Sergei I., et Yuri Manin. 1994. *Homological algebra.* Conversus ex editione Russica (1989) ab auctoribus. Reimpression primae editionis Anglicae ex serie Encyclopaedia of Mathematical Sciences (*Algebra*, V, Encyclopaedia Math. Sci., 38, Springer, Berlin, 1994). Berolini: Springer-Verlag. ISBN 3-540-65378-3. 
*Gelfand, Sergei I., et Yuri Manin. 2003. *Methods of homological algebra.* Conversus ex editione Russica (1988). Editio seconda. Springer Monographs in Mathematics. Berolini: Springer-Verlag. ISBN 3-540-43583-2.
*Geramita, A. V., et Charles Small. 1976. *Introduction to homological methods in commutative rings.* Kingston Ontarii: Queen's University.
*Grandis, Marco. 2012. *Homological algebra: the interplay of homology with distributive lattices and orthodox semigroups.* Singapuae et Hackensack Novae Caesareae: World Scientific. ISBN 9789814407069, ISBN 9814407062.
*Grothendieck, Alexander. 1957. "Sur quelques points d'algèbre homologique." *Tohoku Mathematical Journal* 9 (2): 119–221. doi:10.2748/tmj/1178244839.
*Hilton, Peter, et U. Stammbach. 1997. *A course in homological algebra.* Ed. secunda. Graduate Texts in Mathematics, 4. Novi Eboraci: Springer-Verlag. ISBN 0-387-94823-6.
*Hu, S. T. (Sze-Tsen). 1968. *Introduction to homological algebra.* Franciscopoli: Holden-Day.
*Mac Lane, Saunders. (1975) 1995. *Homology.* Classics in Mathematics. Berolini: Springer-Verlag. ISBN 3-540-58662-8.
*Strooker, Jan R. 1978. *Introduction to categories, homological algebra, and sheaf cohomology.* Cantabrigiae et Novi Eboraci: Cambridge University Press. ISBN 0521216990.
*Weibel, Charles A. 1994. *An introduction to homological algebra.* Cambridge Studies in Advanced Mathematics. 38. Cambridge University Press. ISBN 978-0-521-55987-4. MR 1269324. OCLC 36131259.

## Nexus externi