In mathematics, a commutative ring R is catenary if for any pair of prime ideals p, q, any two strictly increasing chains p = p0 ⊂ p1 ⊂ ... ⊂ pn = q of...

catenoid—the shape assumed by a soap film bounded by two parallel circular rings. The catenary is also called the alysoid, chainette, or, particularly in the materials...

Catenary may refer to: Catenary, a mathematical curve Catenary arch, an arch that follows a catenary curve Catenary ring, a type of mathematical ring...

#formally catenary ring below.) Precisely, a quasi-unmixed ring is a ring in which the unmixed theorem, which characterizes a Cohen–Macaulay ring, holds...

rings, there is the following chain of inclusions. Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings...

rings. For Noetherian local rings, there is the following chain of inclusions. Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃...

Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings A local complete intersection ring is...

rings. For Noetherian local rings, there is the following chain of inclusions: Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃...

universally catenary. Goldie's theorem Given a ring, there is a close connection between the behaviors of injective modules over the ring and whether the ring is...

universally catenary. Excellent rings are one answer to the problem of finding a natural class of "well-behaved" rings containing most of the rings that occur...

the generic freeness plays a main role and the notion of "universally catenary ring" is a key in the proof, see Eisenbud, Ch. 14 of "Commutative algebra...

Practically all noetherian rings that appear in applications are catenary. Ratliff proved that a noetherian local integral domain R is catenary if and only if for...

length. A ring is called universally catenary if any finitely generated algebra over it is catenary. Nagata gave an example of a Noetherian ring which is...

properties of regular rings (such as the property of being universally catenary rings, which means that the (co)dimension of primes is well-behaved), but...

quasi-excellent ring, and if in addition it is universally catenary it is called an excellent ring. A (Noetherian) ring R containing a field k is called geometrically...

semichain modules. The notion of a catenary ring has "chain" as its namesake, but it is in general not related to chain rings. In the 1930s, Gottfried Köthe...

International Congress of Mathematicians in 1966 (Moscow) The Kolchin Catenary Conjecture is a fundamental open problem in differential algebra related...

In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimal surface, meaning...

differential ideal when characteristic sets identify both ideals. The Kolchin catenary conjecture states given a d > 0 {\textstyle d>0} dimensional irreducible...

"Canonical module" is an alternative term for a dualizing module. catenary A ring is called catenary if all maximal chains between two prime ideals have the same...

electric catenary in 1914. This was one of the first electrified lines in Germany. Due to the two world wars and the resulting dismantling of the catenary in...

Kurosh conjecture, the Nullstellensatz and the catenary property for prime ideals. If R is a PI-ring and K is a subring of its center such that R is...

locally noetherian, dimension, catenary, Gorenstein. local complete intersection The local rings are complete intersection rings. See also: regular embedding...

in Georgia Butterfly gantry near Raubling, Germany On the Jakarta Outer Ring Road Gantries placed on either side of the carriageway on the A4 autoroute...

Hennigsdorf (now owned by Bombardier) were used on the line. In 1973, the catenary was removed, although some masts were preserved and reused for the 15 kV...

United States. Clad in stainless steel and built in the form of a weighted catenary arch, it is the world's tallest arch and Missouri's tallest accessible...

stable, covered longeing ring and porter's lodge: the stable has a rectangular base and catenary arches; the longeing ring has a square base with a hyperboloid...

U-shaped pattern. The Pink Line is also known as the Ring Road Line, as the line passes alongside the Ring Road in Delhi. The Pink Line has interchanges with...

influence through the use of white on the walls. It contains a series of sixty catenary arches that creates a space which represents the ribcage of an animal....

The Nuremberg Ring Railway is the ring railway for freight that runs at a distance of three to four kilometres (2 to 2+1⁄2 mi) from the center of Nuremberg...