Hereditary ring

Hereditary ring

In mathematics, especially in the area of abstract algebra known as module theory, a ring "R" is called hereditary if all submodules of projective modules over "R" are again projective. If this is required only for finitely generated submodules, it is called semihereditary.

For a noncommutative ring "R", the terms left (semi-)hereditary (all (finitely generated) submodules of projective "left" "R"-modules are projective) and right (semi-)hereditary are sometimes used. A ring can be left hereditary but not right hereditary, and vice versa.

References

*


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Hereditary nonpolyposis colorectal cancer — Classification and external resources ICD 10 C18 C20 ICD 9 …   Wikipedia

  • Leber's hereditary optic neuropathy — Classification and external resources ICD 10 H47.2 ICD 9 377.16 …   Wikipedia

  • Kula ring — Kula, also known as the Kula exchange or Kula ring, is a ceremonial exchange system conducted in the Milne Bay Province of Papua New Guinea. The Kula ring spans 18 island communities of the Massim archipelago, including the Trobriand Islands and… …   Wikipedia

  • Josias, Hereditary Prince of Waldeck and Pyrmont — Infobox Military Person name= Josias Erbprinz zu Waldeck und Pyrmont lived=birth date|1896|5|13|df=y death date and age|1967|11|30|1896|5|13|df=y placeofbirth=Schloß Schaumburg, Arolsen, German Empire placeofdeath=Schloß Schaumburg, Arolsen,… …   Wikipedia

  • List of mathematics articles (H) — NOTOC H H cobordism H derivative H index H infinity methods in control theory H relation H space H theorem H tree Haag s theorem Haagerup property Haaland equation Haar measure Haar wavelet Haboush s theorem Hackenbush Hadamard code Hadamard… …   Wikipedia

  • RNF139 — Ring finger protein 139, also known as RNF139, is a human gene.cite web | title = Entrez Gene: RNF139 ring finger protein 139| url = http://www.ncbi.nlm.nih.gov/sites/entrez?Db=gene Cmd=ShowDetailView TermToSearch=11236| accessdate = ] PBB… …   Wikipedia

  • china — /chuy neuh/, n. 1. a translucent ceramic material, biscuit fired at a high temperature, its glaze fired at a low temperature. 2. any porcelain ware. 3. plates, cups, saucers, etc., collectively. 4. figurines made of porcelain or ceramic material …   Universalium

  • China — /chuy neuh/, n. 1. People s Republic of, a country in E Asia. 1,221,591,778; 3,691,502 sq. mi. (9,560,990 sq. km). Cap.: Beijing. 2. Republic of. Also called Nationalist China. a republic consisting mainly of the island of Taiwan off the SE coast …   Universalium

  • List of cutaneous conditions — This is an incomplete list, which may never be able to satisfy particular standards for completeness. You can help by expanding it with reliably sourced entries. See also: Cutaneous conditions, Category:Cutaneous conditions, and ICD 10… …   Wikipedia

  • Germany — /jerr meuh nee/, n. a republic in central Europe: after World War II divided into four zones, British, French, U.S., and Soviet, and in 1949 into East Germany and West Germany; East and West Germany were reunited in 1990. 84,068,216; 137,852 sq.… …   Universalium

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”