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The Ring of Fire (also known as the Pacific Ring of Fire, the Rim of Fire, the Girdle of Fire or the Circum-Pacific belt) [note 1] is a tectonic belt of volcanoes and earthquakes. It is about 40,000 km (25,000 mi) long [ 1 ] and up to about 500 km (310 mi) wide, [ 2 ] and surrounds most of the Pacific Ocean .
Divisibility (ring theory) In mathematics, the notion of a divisor originally arose within the context of arithmetic of whole numbers. With the development of abstract rings, of which the integers are the archetype, the original notion of divisor found a natural extension. Divisibility is a useful concept for the analysis of the structure of ...
In algebra, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings; their representations, or, in different language, modules; special classes of rings (group rings, division ...
A division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a nonzero ring [2] in which every nonzero element a has a multiplicative inverse, i.e., an element x with a · x = x · a = 1. Stated differently, a ring is a division ring if and only if its group of units is the set of all nonzero elements.
More generally, any root of unity in a ring R is a unit: if r n = 1, then r n−1 is a multiplicative inverse of r. In a nonzero ring, the element 0 is not a unit, so R × is not closed under addition. A nonzero ring R in which every nonzero element is a unit (that is, R × = R ∖ {0}) is called a division ring (or a skew-field).
An annular solar eclipse will create a stunning “ring of fire” in the sky on October 14, visible to millions living across North, Central and South America.
The Ring of Fire is a vast, mineral-rich region located in the remote James Bay Lowlands of Northern Ontario, Canada. Spanning approximately 5,000 square kilometres (1,900 sq mi), the area is rich in chromite, nickel, copper, platinum group elements, gold, zinc, and other valuable minerals. Discovered in the early 21st century, the Ring of Fire ...
The endomorphism ring of a nonzero right uniserial module has either one or two maximal right ideals. If the module is Artinian, Noetherian, projective or injective, then the endomorphism ring has a unique maximal ideal, so that it is a local ring. The endomorphism ring of an Artinian uniform module is a local ring. [7]