# Questions tagged [associativity]

This is the property shared by many binary operations including group operations. For a binary operation $\cdot$, associativity holds if $(x\cdot y)\cdot z = x \cdot(y\cdot z)$.

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### Matrix Multiplication not associative when matrices are vectors?

Wikipedia states: Given three matrices A, B and C, the products (AB)C and A(BC) are defined if and only the number of columns of A equals the number of rows of B and the number of columns of B ...
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### Associative, non-commutative, non-trivial, analytic binary operation

There was a question whether associative, but non-commutative binary operation over the real numbers exist. A trivial answer is the binary operation $x\circ y = x$ or $x\circ y = y$. As a followup, ...
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### Find or describe all associative algebras possessing only inner derivations.

From cohomology theory we know that separables algebras $A$ possess only inner derivations. In fact, they possess only inner Derivation into every $A$-bimodule $M$ which characterize separable ...
In algebra, we study sets with binary operations satisfying certain properties. However, sometimes that the calculation is undefined for some ordered pairs, such as $a\div 0$ for any complex number $a$...