Flat map

Flat map

The flat map in differential geometry is a name for the mapping that converts coordinate basis vectors into corresponding coordinate 1-forms.

A flat map in ring theory is homomorphism "f" from a ring "R" to a ring "S" if "S" becomes a flat "R"-module when the action of "R" on "S" is given by "f".


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  • Flat morphism — In mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e., : fP : OY,f(P) → OX,P is a flat map …   Wikipedia

  • map projection — noun a projection of the globe onto a flat map using a grid of lines of latitude and longitude • Hypernyms: ↑projection • Hyponyms: ↑conformal projection, ↑orthomorphic projection, ↑conic projection, ↑conical projection, ↑ …   Useful english dictionary

  • Map — /map/, n. Walter, c1140 1209?, Welsh ecclesiastic, poet, and satirist. Also, Mapes /mayps, may peez/. * * * I Graphic representation, drawn to scale and usually on a flat surface, of features usually geographic, geologic, or geopolitical of an… …   Universalium

  • Flat Island (Spratly) — Flat Island or Patag Island ( tl. Patag; zh cp|c=费信岛|p=Feixin Dao; vi. Đảo Bình Nguyên) is the fourteenth largest and second smallest Spratly island. It is the sixth largest among the Philippine occupied Spratly islands. It has an area of 0.57… …   Wikipedia

  • Flat Top — Flat Top, with an elevation of 4,142 feet, is the 20th highest peak in Georgia. It is located in Rabun County, Georgia and is within the boundaries of the Chattahoochee National Forest. There is a view of the rock face of Flat Top from the… …   Wikipedia

  • map — ► NOUN 1) a flat diagram of an area of land or sea showing physical features, cities, roads, etc. 2) a diagram or collection of data showing the arrangement, distribution, or sequence of something. ► VERB (mapped, mapping) 1) represent or record… …   English terms dictionary

  • map — [map] n. [ML mappa (mundi), map (of the world) < L mappa, napkin, cloth (on which maps were painted): said (by QUINTILIAN) to be of Punic orig.; prob. < TalmudHeb mappa < * manpa, contr. < menafa, a fluttering banner] 1. a drawing or… …   English World dictionary

  • Map — (m[a^]p), n. [From F. mappe, in mappemonde map of the world, fr. L. mappa napkin, signal cloth; a Punic word. Cf. {Apron}, {Napkin}, {Nappe}.] 1. A representation of the surface of the earth, or of some portion of it, showing the relative… …   The Collaborative International Dictionary of English

  • Map lichen — Map Map (m[a^]p), n. [From F. mappe, in mappemonde map of the world, fr. L. mappa napkin, signal cloth; a Punic word. Cf. {Apron}, {Napkin}, {Nappe}.] 1. A representation of the surface of the earth, or of some portion of it, showing the relative …   The Collaborative International Dictionary of English

  • Flat Earth — For other uses, see Flat Earth (disambiguation). The Flammarion engraving (1888) depicts a traveller who arrives at the edge of a flat Earth and sticks his head through the firmament …   Wikipedia

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