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...

algebra: an integral domain is a Dedekind domain if and only if it is a hereditary ring; that is, every submodule of a projective module over it is projective...

fir is a right hereditary ring, and likewise a right semifir is a right semihereditary ring. Because projective modules over local rings are free, and...

generated module over a Dedekind domain A (or more generally a semi-hereditary ring) is torsion-free if and only if it is projective; consequently, a finitely...

finding of ring (or ringed) sideroblasts characterizes sideroblastic anemia. Ring sideroblasts are named so because iron-laden mitochondria form a ring around...

is a special feature of hereditary rings like the integers Z: the direct sum of injective modules is injective because the ring is Noetherian, and the...

Hereditary nonpolyposis colorectal cancer (HNPCC) is a hereditary predisposition to colon cancer. HNPCC includes (and was once synonymous with) Lynch...

chamber within the Royal Citadel, its powers only accessible through the hereditary Ring of the Lucii. For centuries, Lucis has been at war with the militaristic...

dynasty by the world's deities in antiquity and accessed through the hereditary Ring of the Lucii. Accordo, located in the southern part of Eos, is an island...

regular ring Quasi-Frobenius ring Hereditary ring, Semihereditary ring Local ring, Semi-local ring Discrete valuation ring Regular local ring Cohen–Macaulay...

Jacques, Hereditary Prince of Monaco, Marquis of Baux (Jacques Honoré Rainier Grimaldi; born 10 December 2014), is the heir apparent to the Monegasque...

Leber's hereditary optic neuropathy (LHON) is a mitochondrially inherited (transmitted from mother to offspring) degeneration of retinal ganglion cells...

Kayser–Fleischer rings (KF rings) are dark rings that appear to encircle the cornea of the eye. They are due to copper deposition in the Descemet's membrane...

finitely generated algebra. hereditary A ring is left hereditary if its left ideals are all projective modules. Right hereditary rings are defined analogously...

ring or Schatzki–Gary ring is a narrowing of the lower esophagus that can cause difficulty swallowing (dysphagia). The narrowing is caused by a ring of...

C*-algebra that is also a Baer *-ring. Since the principal left ideals of a left hereditary ring or left semihereditary ring are projective, it is clear that...

protects Insomnia using a magical barrier called the Wall using the hereditary Ring of the Lucii. Maintaining the Wall drains Regis of his life energy...

most inherited optic neuropathies is permanent and progressive. Leber's hereditary optic neuropathy (LHON) is the most frequently occurring mitochondrial...

operator. A class of rings is called hereditary if every ideal of a ring in the class also belongs to the class. Let R be any ring, not necessarily commutative...

are two classes of hereditary knights in Portugal, the highest grade is the hereditary knight with grand collar. Portuguese hereditary knighthoods confer...

Constriction ring syndrome (CRS) is a congenital disorder with unknown cause. Because of the unknown cause there are many different, and sometimes incorrect...

descendants of Harald. According to the traditional view, Norway was the hereditary kingdom of the 'Fairhair' dynasty, agnatic (patrilineal) descendants of...

Hubertus Georg Eduardo Paolo Nickolos Franz Alois Ignatius Hieronymus Maria, Hereditary Prince of Löwenstein-Wertheim-Rosenberg (30 September 1966 – 24 April...

esophagus"). Endoscopically, ridges, furrows, or rings may be seen in the esophageal wall. Sometimes, multiple rings may occur in the esophagus, leading to the...

A ring name is a type of stage name or nickname used by an athlete such as a professional wrestler, mixed martial artist, or boxer whose real name is considered...

Kula exchange or Kula ring, is a ceremonial exchange system conducted in the Milne Bay Province of Papua New Guinea. The Kula ring was made famous by Bronisław...

father. It is likely that this practice was a factor in the emergence of hereditary heraldry in western Europe in the 12th century. Ecclesiastical seals are...

The Royal House of Durin: Thorin Oakenshield, leader of the Company and hereditary claimant of the kingdom of the Lonely Mountain. He possessed the longest...

cloudiness may have myriad of causes. Corneal opacity that results from hereditary dystrophies is usually symmetric. Corneal enlargement may result from...

medication derived from dihydrotestosterone (DHT). It is used to treat hereditary angioedema. It was developed by American pharmaceutical company Winthrop...