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Fundamentals. The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
Algebra extension. In abstract algebra, an algebra extension is the ring-theoretic equivalent of a group extension . Precisely, a ring extension of a ring R by an abelian group I is a pair ( E, ) consisting of a ring E and a ring homomorphism that fits into the short exact sequence of abelian groups: This makes I isomorphic to a two-sided ideal ...
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Hints About Today's NYT Connections Categories on Tuesday, August 6. 1. These words share a common color. 2. Someone who participates in a study. 3. Actions that show disagreement. 4.
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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 ).
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