additive algebra
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Algebra — This article is about the branch of mathematics. For other uses, see Algebra (disambiguation). Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from… … Wikipedia
Additive category — In mathematics, specifically in category theory, an additive category is a preadditive category C such that any finitely many objects A 1,..., A n of C have a biproduct A 1 ⊕ ⋯ ⊕ A n in C. (Recall that a category C is preadditive if all its… … Wikipedia
Additive inverse — In mathematics, the additive inverse, or opposite, of a number a is the number that, when added to a, yields zero. The additive inverse of a is denoted −a. For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive… … Wikipedia
Additive identity — In mathematics the additive identity of a set which is equipped with the operation of addition is an element which, when added to any element x in the set, yields x . One of the most familiar additive identities is the number 0 from elementary… … Wikipedia
Algebra (ring theory) — In mathematics, specifically in ring theory, an algebra over a commutative ring is a generalization of the concept of an algebra over a field, where the base field K is replaced by a commutative ring R .Any ring can be thought of as an algebra… … Wikipedia
Graded algebra — In mathematics, in particular abstract algebra, a graded algebra is an algebra over a field (or commutative ring) with an extra piece of structure, known as a gradation (or grading ). Graded rings A graded ring A is a ring that has a direct sum… … Wikipedia
Graded Lie algebra — In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra is a Lie algebra which is also a nonassociative graded algebra under the bracket… … Wikipedia
Negation (algebra) — Negation is the mathematical operation that reverses the sign of a number. Thus the negation of a positive number is negative, and the negation of a negative number is positive. The negation of zero is zero. The negation of a number a, usually… … Wikipedia
Von Neumann algebra — In mathematics, a von Neumann algebra or W* algebra is a * algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann,… … Wikipedia
Körper (Algebra) — Ein Körper ist im mathematischen Teilgebiet der Algebra eine ausgezeichnete algebraische Struktur, in der die Addition, Subtraktion, Multiplikation und Division wie bei den „normalen“ reellen Zahlen durchgeführt werden können. Die Bezeichnung… … Deutsch Wikipedia
Measure algebra — In mathematics, a measure algebra is a Boolean algebra with a countably additive positive measure. A probability measure on a measure space gives a measure algebra on the Boolean algebra of measurable sets modulo null sets. Definition A measure… … Wikipedia
