Linear combinationIn mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field, with some generalizations given at the end of the article.
Semiprime ringIn ring theory, a branch of mathematics, semiprime ideals and semiprime rings are generalizations of prime ideals and prime rings. In commutative algebra, semiprime ideals are also called radical ideals and semiprime rings are the same as reduced rings. For example, in the ring of integers, the semiprime ideals are the zero ideal, along with those ideals of the form where n is a square-free integer. So, is a semiprime ideal of the integers (because 30 = 2 × 3 × 5, with no repeated prime factors), but is not (because 12 = 22 × 3, with a repeated prime factor).
Barrier islandBarrier islands are a coastal landforms—a type of dune system and sand island—where an area of sand has been formed by wave and tidal action parallel to the mainland coast. They usually occur in chains, consisting of anything from a few islands to more than a dozen. They are subject to change during storms and other action, but absorb energy and protect the coastlines and create areas of protected waters where wetlands may flourish. A barrier chain may extend for hundreds of kilometers, with islands periodically separated by tidal inlets.
