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algebra with prime characteristic

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  • Characteristic (algebra) — In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring s multiplicative identity element (1) in a sum to get the additive identity element (0); the ring is said… …   Wikipedia

  • Prime ring — In abstract algebra, a non trivial ring R is a prime ring if for any two elements a and b of R , if arb = 0 for all r in R , then either a = 0 or b = 0 . Prime ring can also refer to the subring of a field determined by its characteristic. For a… …   Wikipedia

  • Boolean algebra — This article discusses the subject referred to as Boolean algebra. For the mathematical objects, see Boolean algebra (structure). Boolean algebra, as developed in 1854 by George Boole in his book An Investigation of the Laws of Thought,[1] is a… …   Wikipedia

  • Boolean algebra (introduction) — Boolean algebra, developed in 1854 by George Boole in his book An Investigation of the Laws of Thought , is a variant of ordinary algebra as taught in high school. Boolean algebra differs from ordinary algebra in three ways: in the values that… …   Wikipedia

  • Incidence algebra — In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for any locally finite partially ordered set and commutative ring with unity. Contents 1 Definition 1.1 Related concepts 2 Special elements …   Wikipedia

  • Fundamental theorem of algebra — In mathematics, the fundamental theorem of algebra states that every non constant single variable polynomial with complex coefficients has at least one complex root. Equivalently, the field of complex numbers is algebraically closed.Sometimes,… …   Wikipedia

  • Jordan algebra — In mathematics, a Jordan algebra is defined in abstract algebra as a (usually nonassociative) algebra over a field with multiplication satisfying the following axioms:# xy = yx (commutative law) # (xy)(xx) = x(y(xx)) (Jordan identity)The product… …   Wikipedia

  • Quaternion algebra — In mathematics, a quaternion algebra over a field, F , is a particular kind of central simple algebra, A , over F , namely such an algebra that has dimension 4, and therefore becomes the 2 times;2 matrix algebra over some field extension of F ,… …   Wikipedia

  • Ring of mixed characteristic — In commutative algebra, a ring of mixed characteristic is a commutative ring R having characteristic zero and having an ideal I such that R / I has positive characteristic. Examples The integers Z have characteristic zero, but for any prime… …   Wikipedia

  • Timeline of algebra and geometry — A timeline of algebra and geometryBefore 1000 BC* ca. 2000 BC Scotland, Carved Stone Balls exhibit a variety of symmetries including all of the symmetries of Platonic solids. * 1800 BC Moscow Mathematical Papyrus, findings volume of a frustum *… …   Wikipedia

  • List of Boolean algebra topics — This is a list of topics around Boolean algebra and propositional logic. Contents 1 Articles with a wide scope and introductions 2 Boolean functions and connectives 3 Examples of Boolean algebras …   Wikipedia

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