In mathematics, a semi-local ring is a ring for which R/J(R) is a semisimple ring, where J(R) is the Jacobson radical of R. (Lam 2001, p. §20)(Mikhalev...

specifically in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the...

maximal ideals. 2.  "Semi-local ring" is an archaic term for a Zariski ring. seminormal A seminormal ring is a commutative reduced ring in which, whenever...

its parts. A ring that is a semisimple module over itself is known as an Artinian semisimple ring. Some important rings, such as group rings of finite groups...

Noetherian semi-local ring with 2 maximal ideals, mB (of height 1) and nB (of height 2). Let I be the Jacobson radical of B, and let A = k+I. The ring A is...

the name "semi-local ring" which now means something different, and named "Zariski rings" by Pierre Samuel (1953). Examples of Zariski rings are noetherian...

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

closed points in it. (For Noetherian rings R): R has no prime ideals P such that R/P is a 1-dimensional semi-local ring. Kaplansky, Theorem 31 Amitsur, Shimshon...

mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on (one-sided)...

real closed ring (RCR) is a commutative ring A that is a subring of a product of real closed fields, which is closed under continuous semi-algebraic functions...

In mathematics, an Arf ring was defined by Lipman (1971) to be a 1-dimensional commutative semi-local Macaulay ring satisfying some extra conditions studied...

allows users to discuss local safety and security issues, and share footage captured with Ring products. Via Neighbors, Ring could also provide footage...

M/rad(M). In the case of local rings with maximal ideal P, the top of M is M/PM. In general if R is a semilocal ring (=semi-artinian ring), that is, if R/Rad(R)...

A fairy ring, also known as fairy circle, elf circle, elf ring or pixie ring, is a naturally occurring ring or arc of mushrooms. They are found mainly...

In the area of abstract algebra known as ring theory, a left perfect ring is a type of ring over which all left modules have projective covers. The right...

Zariski ring, such as a Noetherian local ring, is a UFD, then the ring is a UFD. The converse of this is not true: there are Noetherian local rings that...

The ring-tailed lemur (Lemur catta) is a medium- to larger-sized strepsirrhine (wet-nosed) primate and the most internationally recognized lemur species...

he is signed to WWE, where he performs on the SmackDown brand under the ring name JC Mateo. He is best known for his tenure in New Japan Pro-Wrestling...

"Semi-Charmed Life" is a song by American rock band Third Eye Blind from their 1997 eponymous debut studio album. It was released to modern rock radio...

the contest into controversy. Israel was drawn to compete in the second semi-final of the Eurovision Song Contest which took place on 9 May 2024. Performing...

Dendrochronology (or tree-ring dating) is the scientific method of dating tree rings (also called growth rings) to the exact year they were formed in a...

the semi-final allocation draw. The insignia is then traditionally put on display in a public place, such as the city hall or another venue of local significance...

best known for her time as a ring announcer in the professional wrestling promotion WWE from 2021 to 2024 under the ring name Samantha Irvin. Johnson...

The Durban Outer Ring Road is a half ring road that circles the coastal city of Durban, South Africa. It is part of the N2 highway which links the North...

no distinct breeds have been developed yet, can be considered semi-domesticated. The ring-necked pheasant is the state bird of South Dakota, one of only...

A semi-trailer truck (also known by a wide variety of other terms – see below) is the combination of a tractor unit and one or more semi-trailers to carry...

varieties, in the form of modules over local rings, to be studied pointwise as vector spaces over the residue field of the ring. The lemma is named after the Japanese...

the unique ring arcs that exist in this ring. Galatea's mass has been estimated based on the radial perturbations it induces on the ring. Volume derived...

he places the bride's ring on the ring finger of the groom's right hand, and the groom's ring on the bride's finger. The rings are subsequently exchanged...

regular rings should not be confused with the unrelated regular rings and regular local rings of commutative algebra. An element a of a ring is called...