Distributivity mathematics abstract algebra (2 Ergebnisse)

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In mathematics, the theory of fields in abstract algebra lacks a direct product: the direct product of two fields, considered as a ring is never itself a field. On the other hand it is often required to 'join' two fields K and L, either in cases where K and L are given as subfields of a larger field M, or when K and L are both field extensions of a smaller field N (for example a prime field). The tensor product of fields is the best available construction on fields with which to discuss all the phenomena arising. As a ring, it is sometimes a field, and often a direct product of fields; it can, though, contain non-zero nilpotents (see radical of a ring).…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In mathematicsand in particular in abstract algebra, distributivity is a property ofbinary operations that generalises the distributive law from elementaryalgebra. For example: 2 × (1 + 3) = (2 × 1) + (2 × 3). In the left-handside of the above equation, the 2 multiplies the sum of 1 and 3; on theright-hand side, it multiplies the 1 and the 3 individually, with theresults added afterwards. Because these give the same final answer (8)we say that multiplication by 2 distributes over addition of 1 and 3.Since we could have put any real numbers in place of 2, 1, and 3 aboveand still have obtained a true equation, we say that multiplication ofreal numbers distributes over addition of real numbers. Multiplicationof numbers is distributive over addition of numbers, for a broad classof different kinds of numbers ranging from natural numbers to complexnumbers and cardinal numbers.…