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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.
The term "algebraic equation" dates from the time when the main problem of algebra was to solve univariate polynomial equations. This problem was completely solved during the 19th century; see Fundamental theorem of algebra, Abel–Ruffini theorem and Galois theory. Since then, the scope of algebra has been dramatically enlarged.
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras.The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and ...
This is a list of possibly nonassociative algebras.An algebra is a module, wherein you can also multiply two module elements. (The multiplication in the module is compatible with multiplication-by-scalars from the base ring).
The Kansas City Chiefs are looking to make history in Super Bowl 59.. They could become the first team in NFL history to win three consecutive titles, which would augment their legacy as one of ...
Every abelian group is a BCI-algebra, with * defined as group subtraction and 0 defined as the group identity. The subsets of a set form a BCK-algebra, where A*B is the difference A\B (the elements in A but not in B), and 0 is the empty set. A Boolean algebra is a BCK algebra if A*B is defined to be A∧¬B (A does not imply B).
The U.S. Department of Agriculture has spent at least $1.14 billion compensating farmers for the birds they have had to kill. A similar number wasn't immediately available for how much has been ...
In Paris and New York, five-star hotels and Michelin-star restaurants coexist alongside $1 pizza and cheap crepe carts. Aspen — for the most part — lacks the latter.