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Free algebra. In mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since its elements may be described as "polynomials" with non-commuting variables. Likewise, the polynomial ring may be regarded as a free commutative algebra .
v. t. e. In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center of A. This is thus an algebraic structure with an addition, a multiplication, and a scalar multiplication (the multiplication by the image of the ring homomorphism of an element of K ).
Perfect play. In game theory, perfect play is the behavior or strategy of a player that leads to the best possible outcome for that player regardless of the response by the opponent. Perfect play for a game is known when the game is solved. [ 1] Based on the rules of a game, every possible final position can be evaluated (as a win, loss or draw).
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Free objects are the direct generalization to categories of the notion of basis in a vector space. A linear function u : E1 → E2 between vector spaces is entirely determined by its values on a basis of the vector space E1. The following definition translates this to any category. A concrete category is a category that is equipped with a ...
Among Us is an online multiplayer social deduction game developed by an American indie game studio, Innersloth. Among Us is a space-themed game in which a crew of astronauts must complete tasks while trying to figure out who among them is an imposter, who is sabotaging their work and killing the other players.
The splendid fairywren ( Malurus splendens) is a passerine bird in the Australasian wren family, Maluridae. It is found across much of the Australian continent from central-western New South Wales and southwestern Queensland over to coastal Western Australia. It inhabits predominantly arid and semi-arid regions.
e. In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain ), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An algebraic structure may be based on ...