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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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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.
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 ...
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 ...