Search results
Results From The WOW.Com Content Network
Al-Jabr (Arabic: الجبر), also known as The Compendious Book on Calculation by Completion and Balancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلة, al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah; [b] or Latin: Liber Algebræ et Almucabola), is an Arabic mathematical treatise on algebra written in Baghdad around 820 by the Persian polymath ...
Every polynomial ring R[x 1, ..., x n] is a commutative R-algebra. In fact, this is the free commutative R-algebra on the set {x 1, ..., x n}. The free R-algebra on a set E is an algebra of "polynomials" with coefficients in R and noncommuting indeterminates taken from the set E. The tensor algebra of an R-module is naturally an associative R ...
where v 1, v 2, ..., v k are in S, and a 1, a 2, ..., a k are in F form a linear subspace called the span of S. The span of S is also the intersection of all linear subspaces containing S. In other words, it is the smallest (for the inclusion relation) linear subspace containing S. A set of vectors is linearly independent if none is in the span ...
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.